on the structure of specht modules in the principal block of fσ3p abstract let f be a field of characteristic p at least 5 we study the loewy structures of specht modules in the principal block of f 3 p we show that a specht module in the block has loewy length at most 4 and composition length at most 14 furthermore we classify which specht modules have loewy length 1 2 3 or 4 produce a specht module having 14 composition factors describe the second radical layer and the socle of the reducible specht modules and prove that if a specht module corresponds to a partition that is p regular and p restricted then the head of the specht module does not extend the socle

implicit dynamic analysis using an isogeometric reissner mindlin shell formulation summary in isogeometric analysis identical basis functions are used for geometrical representation and analysis in this work non uniform rational basis splines basis functions are applied in an isoparametric approach an isogeometric reissner mindlin shell formulation for implicit dynamic calculations using the galerkin method is presented a consistent as well as a lumped matrix formulation is implemented the suitability of the developed shell formulation for natural frequency analysis is demonstrated by a numerical example in a second set of examples transient problems of plane and curved geometries undergoing large deformations in combination with nonlinear material behavior are investigated via a zero thickness stress algorithm for arbitrary material models a j2 plasticity constitutive law is implemented in the numerical examples the effectiveness robustness and superior accuracy of a continuous interpolation method of the shell director vector is compared with experimental results and alternative numerical approaches copyright 2016 john wiley sons ltd

precise rates in the law of the logarithm for negatively associated random variables let x n n 1 be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance set s email protected k 1 nx k m n max k n s k n 1 suppose s 2 ex 1 email protected k 2 ex 1x k we study the precise rates of a kind of weighted infinite series of p m n email protected snlogn and p s n email protected snlogn as email protected 0 and p m email protected email protected email protected 2n8logn as email protected the results are related to the convergence rates of the law of the logarithm and the chung type law of the logarithm

an isogeometric reissner mindlin shell element based on bezier dual basis functions overcoming locking and improved coarse mesh accuracy abstract we develop a mixed geometrically nonlinear isogeometric reissner mindlin shell element for the analysis of thin walled structures that leverages bezier dual basis functions to address both shear and membrane locking and to improve the quality of computed stresses the accuracy of computed solutions over coarse meshes that have highly non interpolatory control meshes is achieved through the application of a continuous rotational approach the starting point of the formulation is the modified hellinger reissner variational principle with independent displacement membrane and shear strains as the unknown fields to overcome locking the strain variables are interpolated with lower order spline bases while the variations of the strain variables are interpolated with the corresponding bezier dual bases leveraging the orthogonality property of the bezier dual basis the strain variables are condensed out of the system with only a slight increase in the bandwidth of the resulting linear system the condensed approach preserves the accuracy of the non condensed mixed approach but with fewer degrees of freedom from a practical point of view since the bezier dual basis is completely specified through bezier extraction any spline space that admits bezier extraction can utilize the proposed approach directly

on the use of nurbs based discretizations in the scaled boundary finite element method for wave propagation problems abstract we discuss the application of non uniform rational b splines nurbs in the scaled boundary finite element method sbfem for the solution of wave propagation problems at rather high frequencies we focus on the propagation of guided waves along prismatic structures of constant cross section comparisons are made between nurbs based discretizations and high order spectral elements in terms of the achievable convergence rates we find that for the same order of shape functions nurbs can lead to significantly smaller errors compared with lagrange polynomials the difference becomes particularly important at very high frequencies where spectral elements are prone to instabilities furthermore we analyze the behavior of nurbs for the discretization of curved boundaries where the benefit of exact geometry representation becomes crucial even in the low frequency range

p restriction of partitions and homomorphisms between specht modules abstract let be a partition of n we show that the space of f s n homomorphisms between the specht modules s and s r is one dimensional where f is a field of characteristic p and r is the p restriction of equivalently our result proves the corresponding theorem for the homomorphism space hom f s n s reg s where reg is the p regularisation of as defined by james

on a stress resultant geometrically exact shell model part vii shell intersections with dof finite element formulations abstract if the mid surface of a shell is smooth the classical theory describes the orientation of the director field attached to the mid surface by two independent rotational degrees of freedom at a shell intersection where this smoothness assumption no longer holds it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom this added degree of freedom however is totally unrelated to the so called drill rotation widely used as a means of tackling the shell intersection problem a computational procedure involving a trivial modification of the global singularity free update procedure described in part iii of this work is described which completely resolves the shell intersection problem without introducing drill springs or related ad hoc devices the proposed approach leaves unchanged standard finite element formulations in terms of 5 dof node affects only the global update formulae and exhibits excellent performance as illustrated by representative numerical simulations

some q analogues of the carter payne theorem we prove a q analogue of the carter payne theorem for the two special cases cor responding to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows as a consequence we show that these homomorphism spaces are one dimensional when q 6 1 we apply these results to complete the classification of the reducible specht modules for the hecke algebras of the symmetric groups when q 6 1 our methods can also be used to determine certain other pairs of specht modules between which there is a homomorphism in particular we describe the homomorphism space homh s n s for an arbitrary partition s although widely conjectured no q analogue of the full carter payne theorem is known in this paper we prove such an analogue in two important special cases namely when b a 1 or when 1 combinatorially this corresponds to moving an arbitrary number of nodes between adjacent rows or moving one node between an arbitrary number of rows it turns out that our proof has interesting implications we will turn our attention to the classification of the reducible specht modules for the algebras hf q sn when q 6 1 recent work see section 5 3 has resulted in the completion of this classification when q 1 combining our main result theorem 4 5 4 with previously published work we prove that a specht module is reducible if and only if it is e p reducible as defined in definition 5 1 we will also use our discussion of semistandard homomorphisms to obtain a description of the specht modules which contain a submodule isomorphic to the trivial module s n see

an isogeometric continuum shell element for non linear analysis an isogeometric continuum shell formulation is proposed in which nurbs basis functions are used to construct the reference surface of the shell through the thickness behavior is interpolated using a higher order b spline which is in contrast to the standard continuum shell solid like shell formulation where a linear lagrange shape function is typically used in the thickness direction the present formulation yields a complete isogeometric representation of the continuum shell the shell element is implemented in a standard finite element code using bezier extraction which facilitates numerical integration on the reference surface of the shell through the thickness integration is done using a connectivity array which determines the support of a b spline basis function over an element the formulation has been verified using different linear and geometrically non linear examples the ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated

the ordinary quiver of a weight three block of the symmetric group is bipartite abstract suppose f is a field of characteristic p 5 and that b is a p block of the symmetric group s n of defect 3 we prove that the ext 1 quiver of b is bipartite with the bipartition being described in a simple way using the leg lengths of p hooks of partitions

quantum weyl reciprocity and tilting modules quantum weyl reciprocity relates the representation theory of hecke algebras of type a with that of q schur algebras this paper establishes that weyl reciprocity holds integrally i e over the ring q q 1 of laurent polynomials and that it behaves well under base change a key ingredient in our approach involves the theory of tilting modules for q schur algebras new results obtained in that direction include an explicit determination of the ringel dual algebra of a q schur algebra in all cases in particular in the most interesting situation the ringel dual identifies with a natural quotient algebra of the hecke algebra

irreducible specht modules are signed young modules recently donkin defined signed young modules as a simultaneous generalization of young and twisted young modules for the symmetric group we show that in odd characteristic if a specht module s is irreducible then s is a signed young module thus the set of irreducible specht modules coincides with the set of irreducible signed young modules this provides evidence for our conjecture that the signed young modules are precisely the class of indecomposable self dual modules with specht filtrations the theorem is false in characteristic two

a hierarchic family of isogeometric shell finite elements a hierarchic family of isogeometric shell finite elements based on nurbs shape functions is presented in contrast to classical shell finite element formulations inter element continuity of at least c1 enables a unique and continuous representation of the surface normal within one nurbs patch this does not only facilitate formulation of kirchhoff love type shell models for which the standard galerkin weak form has a variational index of 2 but it also offers significant advantages for shear deformable reissner mindlin type shells and higher order shell models for a 5 parameter shell formulation with reissner mindlin kinematics a hierarchic difference vector which accounts for shear deformations is superimposed onto the rotated kirchhoff love type director of the deformed configuration this split into bending and shear deformations in the shell kinematics results in an element formulation which is free from transverse shear locking without the need to apply further remedies like reduced integration assumed natural strains or mixed finite element formulations the third member of the hierarchy is a 7 parameter model including thickness change and allowing for application of unmodified three dimensional constitutive laws the phenomenon of curvature thickness locking coming along with this kinematic extension again is automatically avoided by the hierarchic difference vector concept without any further treatment membrane locking and in plane shear locking are removed by two different approaches firstly elimination via the discrete strain gap dsg method and secondly removal of parasitic membrane strains using a hybrid mixed method based on the hellinger reissner variational principle the hierarchic kinematic structure of the three different shell formulations allows a straightforward combination of these elements within one mesh and is thus the ideal basis for a model adaptive approach

on the almost sure behavior of sums of iid random variables in hilbert space we study the almost sure behavior of sums of operatorname iid random variables satisfying the bounded lil in hilbert space we show that the almost sure behavior is different from the gaussian case whenever the second strong moments are infinite a law of the k times iterated logarithm is established which refines the bounded lil the interesting feature here is that contrary to the known conditions for the bounded lil one needs not only moment type conditions but also a nice structure of the covariance operator

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

irreducible projective representations of the alternating group which remain irreducible in characteristic 2 abstract for any finite group g it is an interesting question to ask which ordinary irreducible representations of g remain irreducible in a given characteristic p we answer this question for p 2 when g is the proper double cover of the alternating group as a key ingredient in the proof we prove a formula for the decomposition numbers in rouquier blocks of double covers of symmetric groups in terms of schur p functions

the darling erdős theorem for sums of i i d random variables we obtain a general darling erd s type theorem for the maximum of appropriately normalized sums of i i d mean zero r v s with finite variances we infer that the darling erd s theorem holds in its classical formulation if and only ife x21 x t o loglogt 1 ast our method is based on an extension of the truncation techniques of feller 1946 to non symmetric r v s as a by product we are able to reprove fundamental results of feller 1946 dealing with lower and upper classes in the hartman wintner lil

the breuil mezard conjecture when l neq p let l and p be primes let f qp be a finite extension with absolute galois group gf let f be a finite field of characteristic l and let w gf gln f be a continuous representation let r be the universal framed deformation ring for if l d p then the breuil mezard conjecture as recently formulated by emerton and gee relates the mod l reduction of certain cycles in r to the mod l reduction of certain representations of gln of we state an analogue of the breuil mezard conjecture when l p and we prove it whenever l 2 using automorphy lifting theorems we give a local proof when l is quasibanal for f and is tamely ramified we also analyze the reduction modulo l of the types defined by schneider and zink

on the decomposition numbers of the ree groups f42 q2 in non defining characteristic abstract we compute the l modular decomposition matrices of the simple ree groups f 4 2 q 2 where q 2 2 2 n 1 and n 0 for all primes l 3 up to some entries in the unipotent and one entry in the non unipotent characters we determine the smallest degree of a nontrivial irreducible l modular representation of f 4 2 q 2 for all primes l 3 and also obtain results on the 3 modular decomposition matrices of f 4 2 q 2

character values and decomposition matrices of symmetric groups the relationships between the values taken by ordinary characters of symmetric groups are exploited to prove two theorems in the modular representation theory of the symmetric group 1 the decomposition matrices of symmetric groups in odd characteristic have distinct rows in characteristic 2 the rows of a decomposition matrix labelled by the different partitions and are equal if and only if and are conjugate an analogous result is proved for hecke algebras 2 a specht module for the symmetric group sn defined over an algebraically closed field of odd characteristic is decomposable on restriction to the alternating group an if and only if it is simple and the labelling partition is self conjugate this result is generalised to an arbitrary field of odd characteristic

decomposition matrices for low rank unitary groups we study the decomposition matrices of the unipotent blocks of finite special unitary groups sun q for unitary primes larger than n up to few unknown entries we give a complete solution for n 2 10 we also prove a general result for two column partitions when divides q 1 this is achieved using projective modules coming from the adic cohomology of deligne lusztig varieties

an efficient and robust rotational formulation for isogeometric reissner mindlin shell elements abstract this work is concerned with the development of an efficient and robust isogeometric reissner mindlin shell formulation for the mechanical simulation of thin walled structures such structures are usually defined by non uniform rational b splines nurbs surfaces in industrial design software the usage of isogeometric shell elements can avoid costly conversions from nurbs surfaces to other surface or volume geometry descriptions the shell formulation presented in this contribution uses a continuous orthogonal rotation described by rodrigues tensor in every integration point to compute the current director vector the rotational state is updated in a multiplicative manner large deformations and finite rotations can be described accurately the proposed formulation is robust in terms of stable convergence behavior in the nonlinear equilibrium iteration for large load steps and geometries with large and arbitrary curvature and in terms of insensitivity to shell intersections with kinks under small angles three different integration schemes and their influence on accuracy and computational costs are assessed the efficiency and robustness of the proposed isogeometric shell formulation is shown with the help of several examples accuracy and efficiency is compared to an isogeometric shell formulation with the more common discrete rotational concept and to lagrange based finite element shell formulations the competitiveness of the proposed isogeometric shell formulation in terms of computational costs to attain a pre defined error level is shown

precise asymptotics for the linear processes generated by associated random variables in hilbert spaces let e k k z be a strictly stationary associated sequence of random variables taking values in a real separable hilbert space and a k k z be a sequence of bounded linear operators for a linear process x k i a i e k i the precise probability and moment convergence rates of i 1 nx i in some limit theorems are discussed

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

reducible specht modules abstract james and mathas conjecture a criterion for the specht module s for the symmetric group to be irreducible over a field of prime characteristic we extend a result of lyle to prove this conjecture in one direction our techniques are elementary

computational aspects of vector like parametrization of three dimensional finite rotations theoretical and computational aspects of vector like parametrization of three dimensional finite rotations which uses only three rotation parameters are examined in detail in this work the relationship of the proposed parametrization with the intrinsic representation of finite rotations via an orthogonal matrix is clearly identified careful considerations of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations are presented for the chosen model problem of reissner s non linear beam theory pertaining details of numerical implementation are discussed for the simplest choice of the finite element interpolations for a 2 node three dimensional beam element a number of numerical simulations in three dimensional finite rotation analysis are presented in order to illustrate the proposed approach

symmetric group blocks of small defect has a specht module s and a p modular irreducible module d the decomposition number s d is de ned to be the composition multiplicity of d in s the following facts areknown about blocks of weight w a if w 0 or 1 then all the decomposition numbers of the block are 0 or 1 b if w 2 and p 2 then all the decomposition numbers of the block are 0 or 1 s2 c if w 4 then some decomposition numbers of a block can be greater than 1 even if p w moreover if w 0 1 or 2 then there is a known method for determining the decompositionnumbers r the situation for the case w 3 is still not properly understood in particular thedecomposition number s 2p 2 2p 2 p 1 1 d 3p 3 2p 1 is yet to be determined for p 5 this is just one of a collection of decomposition numbers forweight 3 which we are unable to evaluate our investigation of blocks of weight 3 grew out of an attempt to improve upon the earlier resultsof martin and russell mr by explicitly calculating the decomposition numbers this led us todiscover various errors and omissions in mr which place in doubt the claim made there that whenp w all the decomposition numbers are 0 or 1 note incidentally that if the decompositionnumbers for a given block are known to be 0 or 1 then the decomposition numbers can in principle be determined by applying schaper s theorem sch jm1 2 basic resultsby using a result of brundan and kleshchev we are able to improve upon the presentation ofseveral of the basic techniques used in s1 s2 mr for estimating decomposition numbers in orderto state these results recall that the diagram of a partition is the set of nodes i j 1 j

signed young modules and simple specht modules abstract by a result of hemmer every simple specht module of a finite symmetric group over a field of odd characteristic is a signed young module while specht modules are parametrized by partitions indecomposable signed young modules are parametrized by certain pairs of partitions the main result of this article establishes the signed young module labels of simple specht modules along the way we prove a number of results concerning indecomposable signed young modules that are of independent interest in particular we determine the label of the indecomposable signed young module obtained by tensoring a given indecomposable signed young module with the sign representation as consequences we obtain the green vertices green correspondents cohomological varieties and complexities of all simple specht modules and a class of simple modules of symmetric groups and extend the results of gill on periodic young modules to periodic indecomposable signed young modules

a mixed shell formulation accounting for thickness strains and finite strain 3d material models a non linear quadrilateral shell element for the analysis of thin structures is presented the reissner mindlin theory with inextensible director vector is used to develop a three field variational formulation with independent displacements stress resultants and shell strains the interpolation of the independent shell strains consists of two parts the first part corresponds to the interpolation of the stress resultants within the second part independent thickness strains are considered this allows incorporation of arbitrary non linear 3d constitutive equations without further modifications the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison with other element formulations we present results for finite strain elasticity inelasticity bifurcation and post buckling problems copyright 2007 john wiley sons ltd

precise rates in the law of the logarithm in the hilbert space let fx xn n 1g be a sequence of i i d random variables taking values in a real separable hilbert space h k k with covariance operator and set sn x1 xn n 1 let an o p n logn we prove that for any 1 id 2 lim p ri1 2 i r i 1 a d 2 1 x n 1 n ri2 logn a p n

james regularization theorem for double covers of symmetric groups abstract this paper is concerned with the modular representation theory of schur s double covers of symmetric groups we establish an analogue of james regularization theorem which describes leading terms for branching multiplicities and decomposition numbers with respect to the usual dominance ordering

isogeometric mortar methods the application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically for the lagrange multiplier two choices of uniformly stable spaces are presented both of them are spline spaces but of a different degree in one case we consider an equal order pairing for which a cross point modification based on a local degree reduction is required in the other case the degree of the dual space is reduced by two compared to the primal this pairing is proven to be inf sup stable without any necessary cross point modification several numerical examples confirm the theoretical results and illustrate additional aspects

irreducibility of induced supermodules for general linear supergroups abstract in this note we determine when an induced supermodule h g 0 corresponding to a dominant integral highest weight of the general linear supergroup g g l m n is irreducible using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of weyl supermodules v this extends the result of kac 12 13 who proved that for ground fields of characteristic zero v is irreducible if and only if is typical

precise asymptotics in the law of the iterated logarithm let x x 1 x 2 be i i d random variables with mean 0 and positive finite variance 2 and set s n x 1 x n n 1 continuing earlier work related to strong laws we prove the following analogs for the law of the iterated logarithm lim e 2 2 2 n 3 1 n p s n e n log log n a n 2 e 2 whenever a n o n log log n for some y 1 2 assuming slightly more than finite variance and lim e 2 1 n log n p s n e n log log n 2

projective modules for the symmetric group and young s seminormal form abstract we study the representation theory of the symmetric group s n in positive characteristic p using features of the llt algorithm we give a conjectural description of the projective cover p of the simple module d where is a p restricted partition such that all ladders of the corresponding ladder partition are of order less than p inspired by the recent theory of klr algebras we explain an algorithm that allows us to verify this conjectural description for n 15 at least

filtrations in rouquier blocks of symmetric groups and schur algebras we study rouquier blocks of symmetric groups and schur algebras in detail and obtain explicit descriptions for the radical layers of the principal indecomposable weyl young and specht modules of these blocks at the same time the jantzen filtrations of the weyl modules are shown to coincide with their radical filtrations we also address the conjectures of martin lascoux leclerc thibon rouquier and james for these blocks

martin s conjecture holds for weight 3 blocks of symmetric groups abstract we prove that martin s conjecture holds for weight 3 blocks of symmetric group algebras that if these blocks have abelian defect group then their projective indecomposable modules have a common radical length 7

improved numerical integration for locking treatment in isogeometric structural elements part i beams a general mathematical framework is proposed in this paper to define new quadrature rules in the context of bb spline nurbs based isogeometric analysis high order continuity across the elements within a patch turned out to have higher accuracy than c0c0 finite elements as well as a better time efficiency unfortunately a maximum regularity accentuates the shear and membrane locking in thick structural elements the improved selective reduced integration schemes are given for uni dimensional beam problems with basis functions of order two and three and can be easily extended to higher orders the resulting bb spline nurbs finite elements are free from membrane and transverse shear locking moreover no zero energy modes are generated the performance of the approach is evaluated on the classical test of a cantilever beam subjected to a distributed moment and compared to lagrange under integrated finite elements

the principal 3 blocks of four and five dimensional projective special linear groups in non defining characteristic abstract in representation theory of finite groups there is a well known and important conjecture due to m broue he has conjectured that for any prime p if a finite group g has an abelian sylow p subgroup p then the principal p blocks of g and the normalizer ng p of p in g are derived equivalent let q be a power of a prime such that q 2 or 5 mod 9 in this paper we show that broue s conjecture is true for p 3 and for g psl4 q and g psl5 q in these cases g has elementary abelian sylow 3 subgroups of order 9 what we prove here is the following in the case g psl4 q all the principal 3 blocks of g are morita even puig equivalent independently of infinitely many q in the case g psl5 q all the principal 3 blocks of g are morita even puig equivalent to the principal 3 block of ng p independently of infinitely many q

irreducible specht modules for hecke algebras of type a abstract let f be a field n a non negative integer a partition of n and s the corresponding specht module for the iwahori hecke algebra h f q s n james and mathas conjecture a necessary and sufficient condition on for s to be irreducible we prove the sufficiency of this condition in the case where f has infinite characteristic and also in the case where q 1

precise asymptotics in complete moment convergence for self normalized sums let x x 1 x 2 be a sequence of nondegenerate i i d random variables with zero means set s n x 1 x n and v n 2 x 1 2 x n 2 ex 2i x x is a slowly varying function at we prove that for any b 2 d 2 b 1 email protected email protected b d 1 email protected n 2 logn d 2 bne s n v n 2i s n email protected n logn 1 b email protected n b d 1 b d 1 2 where n is a standard normal random variable

precise asymptotics in the baum katz and davis laws of large numbers let x x1 x2 be a sequence of i i d random variables such that ex 0 let z be a random variable possessing a stable distribution g with exponent 1 2 assume the distribution of x is attracted to g and set sn x1 xn we prove that n 1nr p 2p sn en1 p e p p r p 1 pr pe z p p r p 1 as e 0 for 1 p r under the additional assumption that there is normal attraction to g and that n 11np sn en1 p p p logeas e 0 for 1 p we close with a related result for the limiting case r p 2

some reducible specht modules for iwahori hecke algebras of type a with q 1 abstract let p be a prime and f a field of characteristic p and let h n denote the iwahori hecke algebra of the symmetric group s n over f at q 1 we prove that there are only finitely many partitions such that both and are 2 singular and the specht module s for h is irreducible

adjustment matrices for weight three blocks of iwahori hecke algebras abstract we compute the adjustment matrices for weight 3 blocks of iwahori hecke algebras of type a in characteristic 2 or 3 this enables all the decomposition numbers for weight 3 blocks to be calculated

on torsion in the intersection cohomology of schubert varieties abstract we prove that the prime torsion in the local integral intersection cohomology of schubert varieties in the flag variety of the general linear group grows exponentially in the rank the idea of the proof is to find a highly singular point in a schubert variety and calculate the euler class of the normal bundle to the miraculously smooth fibre in a particular bott samelson resolution the result is a geometric version of an earlier result established using soergel bimodule techniques

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

globally irreducible weyl modules abstract in the representation theory of split reductive algebraic groups it is well known that every weyl module with minuscule highest weight is irreducible over every field also the adjoint representation of e 8 is irreducible over every field in this paper we prove a converse to these statements as conjectured by gross if a weyl module is irreducible over every field it must be either one of these or trivially constructed from one of these we also prove a related result on non degeneracy of the reduced killing form

sp6 2a is good for the mckay alperin weight and related local global conjectures abstract the so called local global conjectures in the representation theory of finite groups relate the representation theory of g to that of certain proper subgroups such as the normalizers of particular p groups recent results by several authors reduce some of these conjectures to showing that a certain collection of stronger conditions holds for all finite simple groups here we show that g sp 6 2 a is good for these reductions for the mckay conjecture the alperin weight conjecture and their blockwise versions

theory and numerics of three dimensional beams with elastoplastic material behaviour a theory of space curved beams with arbitrary cross sections and an associated finite element formulation is presented within the present beam theory the reference point the centroid the centre of shear and the loading point are arbitrary points of the cross section the beam strains are based on a kinematic assumption where torsion warping deformation is included each node of the derived finite element possesses seven degrees of freedom the update of the rotational parameters at the finite element nodes is achieved in an additive way applying the isoparametric concept the kinematic quantities are approximated using lagrangian interpolation functions since the reference curve lies arbitrarily with respect to the centroid the developed element can be used to discretize eccentric stiffener of shells due to the implemented constitutive equations for elastoplastic material behaviour the element can be used to evaluate the load carrying capacity of beam structures copyright 2000 john wiley sons ltd

hecke algebras of typeawithq 1 abstract in this paper we study the decomposition matrices of the hecke algebras of type a with q 1 over a field of characteristic 0 we give explicit formulae for the columns of the decomposition matrices indexed by all 2 regular partitions with 1 or 2 parts and an algorithm for calculating the columns of the decomposition matrix indexed by partitions with 3 parts combining these results we find all of the rows of the decomposition matrices which are indexed by partitions with at most four parts all this is accomplished by means of a more general theory which begins by showing that the decomposition numbers in the columns of the decomposition matrices indexed by 2 regular partitions with enormous 2 cores are littlewood richardson coefficients

a kind of complete moment convergence for self normalized sums let x x n n 1 be a sequence of independent and identically distributed i i d random variables with x in the domain of attraction of the normal law and ex 0 in this note we obtain a new kind of complete moment convergence for self normalized sums

a robust non linear mixed hybrid quadrilateral shell element in the paper a non linear quadrilateral shell element for the analysis of thin structures is presented the variational formulation is based on a hu washizu functional with independent displacement stress and strain fields the interpolation matrices for the mid surface displacements and rotations as well as for the stress resultants and strains are specified restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test using newton s method the finite element approximation of the stationary condition is iteratively solved our formulation can accommodate arbitrary non linear material models for finite deformations in the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post buckling response the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison to other element formulations copyright 2005 john wiley sons ltd

weights of multipartitions and representations of ariki koike algebras abstract we consider representations of the ariki koike algebra a q deformation of the group algebra of the complex reflection group c r s n the representations of this algebra are naturally indexed by multipartitions of n and for each multipartition we define a non negative integer called the weight of we prove some basic properties of this weight function and examine blocks of small weight

a coupled two scale shell model with applications to layered structures summary in this paper a coupled two scale shell model is presented a variational formulation and associated linearization for the coupled global local boundary value problem is derived for small strain problems various numerical solutions are computed within the so called fe 2 method the discretization of the shell is performed with quadrilaterals whereas the local boundary value problems at the integration points of the shell are discretized using 8 noded or 27 noded brick elements or so called solid shell elements at the bottom and top surface of the representative volume element stress boundary conditions are applied whereas at the lateral surfaces the in plane displacements are prescribed for the out of plane displacements link conditions are applied the coupled nonlinear boundary value problems are simultaneously solved within a newton iteration scheme with an important test the correct material matrix for the stress resultants assuming linear elasticity and a homogeneous continuum is verified copyright 2013 john wiley sons ltd

q analogues of regularisation theorems for linear and projective representations of the symmetric group abstract brundan and kleshchev have recently proved an analogue of james s regularisation theorem for modular representations of symmetric groups in the context of projective representations we prove q analogues of both theorems i e corresponding theorems concerning canonical basis coefficients for basic representations of quantum affine algebras of types a e 1 1 and a 2 n 2

the irreducible representations of the alternating group which remain irreducible in characteristic p let p be an odd prime and an the alternating group of degree n we determine which ordinary irreducible representations of u n remain irreducible in characteristic p verifying the author s conjecture from 2010 given the preparatory work done in 2010 our task is to determine which self conjugate partitions label specht modules for the symmetric group in characteristic p having exactly two composition factors this is accomplished through the use of the robinson brundan kleshchev i restriction functors together with known results on decomposition numbers for the symmetric group and additional results on the mullineux map and homomorphisms between specht modules

isogeometric reissner mindlin shell analysis with exactly calculated director vectors abstract an isogeometric reissner mindlin shell derived from the continuum theory is presented the geometry is described by nurbs surfaces the kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system hence the definition of nodal basis systems at the control points is necessary for the proposed formulation the control points are in general not located on the shell reference surface and thus several choices for the nodal values are possible the proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof thus the initial director vector coincides with the normal vector even for the coarsest mesh in addition to that a more accurate interpolation of the current director and its variation is proposed instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation the exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes the convergence behavior is shown to be correct for k refinement allowing the use of coarse meshes with high orders of nurbs basis functions this is potentially advantageous for applications with high numerical effort per integration point the geometrically nonlinear formulation accounts for large rotations the consistent tangent matrix is derived various standard benchmark examples show the superior accuracy of the presented shell formulation a new benchmark designed to test the convergence behavior for free form surfaces is presented despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

schubert calculus and torsion explosion the author observes that certain numbers occurring in schubert calculus for sl also occur as entries in intersection forms controlling decompositions of soergel bimodules in higher rank these numbers grow exponentially this observation gives many counter examples to the expected bounds in lusztig s conjecture on the characters of simple rational modules for sl over fields of positive characteristic the examples also give counter examples to the james conjecture on decomposition numbers for symmetric groups

specht modules labelled by hook bipartitions i abstract brundan kleshchev and wang equip the specht modules s over the cyclotomic khovanov lauda rouquier algebra h n with a homogeneous z graded basis in this paper we begin the study of graded specht modules labelled by hook bipartitions n m 1 m in level 2 of h n which are precisely the hecke algebras of type b with quantum characteristic at least three we give an explicit description of the action of the khovanov lauda rouquier algebra generators 1 n 1 on the basis elements of s n m 1 m introducing certain specht module homomorphisms we construct irreducible submodules of these specht modules and thereby completely determine the composition series of specht modules labelled by hook bipartitions

dual and approximate dual basis functions for b splines and nurbs comparison and application for an efficient coupling of patches with the isogeometric mortar method abstract this contribution defines and compares different methods for the computation of dual basis functions for b splines and non uniform rational b splines nurbs they are intended to be used as test functions for the isogeometric mortar method but other fields of application are possible too three different concepts are presented and compared the first concept is the explicit formula for the computation of dual basis functions for nurbs proposed in the work of carl de boor these dual basis functions entail minimal support i e the support of the dual basis functions is equal to the support of the corresponding b spline basis functions in the second concept dual basis functions are derived from the inversion of the gram matrix these dual basis functions have global support along the interface the third concept is the use of approximate dual basis functions which were initially proposed for the use in harmonic analysis the support of these functions is local but larger than the support of the associated b spline basis functions we propose an extension of the approximate dual basis functions for nurbs basis functions after providing the general formulas we elaborate explicit expressions for several degrees of spline basis functions all three approaches are applied in the frame of the mortar method for the coupling of non conforming nurbs patches a method which allows complex discretizations with multiple intersecting interfaces is presented numerical examples show that the explicitly defined dual basis functions with minimal support severely deteriorate the global stress convergence behavior of the mechanical analysis this fact is in accordance with mathematical findings in literature which state that the optimal reproduction degree of arbitrary functions is not possible without extending the support of the dual basis functions the dual basis functions computed from the inverse of the gram matrix yield accurate numerical results but the global support yields significantly higher computational costs in comparison to computations of conforming meshes only the approximate dual basis functions yield accurate and efficient computations where neither accuracy nor efficiency is significantly deteriorated in comparison to computations of conforming meshes all basic cases of t intersections and star intersections are studied furthermore an example which combines all basic cases in a complex discretization is given the applicability of the presented method for the nonlinear case and for shell formulations is shown with the help of one numerical example

bounds on the dimension of ext for finite groups of lie type abstract let g be a finite group of lie type defined in characteristic p and let k be an algebraically closed field of characteristic r 0 we will assume that r p so we are in the non defining characteristic case let v be a finite dimensional irreducible left kg module in 2011 guralnick and tiep found bounds on the dimension of h 1 g v in non defining characteristic which are independent of v the aim of this paper is to generalize the work of gurlanick and tiep we assume that g is split and use methods of modular harish chandra theory to find bounds on the dimension of ext k g 1 y v where y and v are irreducible kg modules we then use dipper and du s algorithms to illustrate our bounds in a series of examples

some reducible specht modules we wish to consider which ordinary irreducible representations of the symmetric group sn remain irreducible modulo a prime p this is the same as asking which partitions of n have the property that the corresponding specht module s is reducible over a field of characteristic p if or its conjugate partition is p regular then the answer is known 6 8 it is also known in the case p 2 7 this paper discusses some of the reducible specht modules in the case that p 3 throughout p will be an odd prime and a partition of some integer n we will prove some cases of a conjecture by james and mathas 9 given below we begin with some definitions

efficient isogeometric nurbs based solid shell elements mixed formulation and b method abstract in this work solid shell nurbs elements are developed in order to address static problems of slender structures under small perturbations a single layer of elements is considered through the thickness of the shell and the degree of approximation in that direction is chosen to be equal to two a full 3d constitutive relation is assumed the objective is to obtain highly accurate low degree elements to be used in coarse meshes in order to do that we propose a mixed method from which we derive a b projection to deal with locking the main idea is to modify the interpolation of the average stresses and strains through the thickness more precisely we develop two finite elements the first element which is based on the mixed method or equivalently on the b projection is extremely accurate but leads to a fully populated global stiffness matrix to improve the efficiency the second element uses a local least squares type procedure to define a new b projection leading to a sparse global stiffness matrix the quality and efficiency of the methods are assessed through several usual test cases and by comparison with other published techniques

some new decomposable specht modules abstract we present with proof a new family of decomposable specht modules for the symmetric group in characteristic 2 these specht modules are labelled by partitions of the form a 3 1 b and are the first new examples found for thirty years our method of proof is to exhibit summands isomorphic to irreducible specht modules by constructing explicit homomorphisms between specht modules

the weak substitution method an application of the mortar method for patch coupling in nurbs based isogeometric analysis in this contribution a mortar type method for the coupling of non conforming nurbs surface patches is proposed the connection of non conforming patches with shared degrees of freedom requires mutual refinement which propagates throughout the whole patch due to the tensor product structure of nurbs surfaces thus methods to handle non conforming meshes are essential in nurbs based isogeometric analysis the main objective of this work is to provide a simple and efficient way to couple the individual patches of complex geometrical models without altering the variational formulation the deformations of the interface control points of adjacent patches are interrelated with a master slave relation this relation is established numerically using the weak form of the equality of mutual deformations along the interface with the help of this relation the interface degrees of freedom of the slave patch can be condensated out of the system a natural connection of the patches is attained without additional terms in the weak form the proposed method is also applicable for nonlinear computations without further measures linear and geometrical nonlinear examples show the high accuracy and robustness of the new method a comparison to reference results and to computations with the lagrange multiplier method is given

homomorphisms between specht modules in positive characteristic the specht modules s corresponding to partitions are not necessarily irreducible and understanding their structure is vital to understanding the representation theory of the symmetric group in this paper we address the related problem of finding the spaces of homomorphisms between specht modules indeed in 2 carter and payne showed that the space of homomorphisms from s to s is non zero for certain pairs of partitions and where the young diagram for is obtained from that for by moving several nodes from one row to another we also consider partitions of this type and by explicitly examining certain combinations of semi standard homomorphisms we are able to give a constructive proof of the carter payne theorem and to generalise it