generation and random generation from simple groups to maximal subgroups abstract let g be a finite group and let d g be the minimal number of generators for g it is well known that d g 2 for all non abelian finite simple groups we prove that d h 4 for any maximal subgroup h of a finite simple group and that this bound is best possible we also investigate the random generation of maximal subgroups of simple and almost simple groups by applying a recent theorem of jaikin zapirain and pyber we show that the expected number of random elements generating such a subgroup is bounded by an absolute constant we then apply our results to the study of permutation groups in particular we show that if g is a finite primitive permutation group with point stabilizer h then d g 1 d h d g 4

intertwining operators and unitary representations i abstract for a linear semisimple lie group with a compact cartan subgroup the authors obtain formulas for the action of intertwining operators on certain subspaces of standard induced representations these formulas provide explicit limitations on the pool of candidates for irreducible unitary representations since the only possible invariant inner product is given by such an intertwining operator

on the probability of generating a monolithic group abstract a group l is primitive monolithic if l has a unique minimal normal subgroup n and trivial frattini subgroup by p l n k we denote the conditional probability that k randomly chosen elements of l generate l given that they project onto generators for l n in this article we show that p l n k is controlled by p y s 2 where n s r and y is a 2 generated almost simple group with socle s that is contained in the normalizer in l of the first direct factor of n information about p l n k for l primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups

spherical unitary highest weight representations in this paper we give an almost complete classification of the h spherical unitary highest weight representations of a hermitian lie group g where g h is a symmetric space of cayley type

analysis in space time bundles iii higher spin bundles the universal cosmos m is the unique four dimensional globally causal space time manifold to which the dirac and maxwell equations among others maximally and covariantly extend a systematic treatment is presented of general fields over m of arbitrary spin considered are fields induced from all irreducible representation of the isotropy group scale extended poincare group to g the connected causal group of m restricted to any species of such fields the k invariant canonical dirac operator k maximal essentially compact subgroup of g is shown g covariant for a unique conformal weight a normalized k finite basis for such fields is constructed the basis actions thereon of the dirac operator infinitesimal generators of g discrete symmetries second order casimir and the essentially unique third order noncentral quantum number enveloping algebra element invariant under k are derived composition series under g of a class of these field spaces namely the extension to m of the relativistic fields considered by bargman and wigner or arbitrary spin and conformal weight are determined distinguishing by invariance and causality features alone the essentially conventional positive energy mass 0 subspaces and massive invariant sub quotient spaces whose unitarity under g is given a new proof the completely positive subclass cf below of representations is determined a more detailed treatment of spin one bundles vector and two form of arbitrary conformal weight is included the exterior derivative transformations are diagonalized and the conformally invariant massive spin one scalar product is identified with a mathematical version of the conventional electromagnetic field lagrangian

high order finite elements for shells in this article the p version finite element method is applied to thin walled structures two different hierarchic element formulations are compared a shell approach as well as a shell like solid formulation both approaches are compared for linear elastic and elastoplastic problems special emphasis is placed on the efficiency as well as on determining the area of application for both formulations

an integral transform in l2 cohomology for the ladder representations of u p q starting from the realization of the fock space as l2 cohomology of cp q h0 p cp q m zhm0 p cp q an integral transform is constructed which is a direct image mapping from hm0 p cp q into the space of holomorphic sections of some vector bundle em over m u p q u q u p m 0 the transform intertwines the natural actions of u p q and is injective if m 0 so it provides a geometric realization of the ladder representations of u p q the sections in the image of the transform satisfy certain linear differential equations which are explicitly described for example maxwell s equations are of this form if p q 2 and m 2 thus this transform is analogous to the penrose correspondence

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

classification of minimal representations of real simple lie groups based on an idea by gan and savin represent theory 9 46 93 2005 we give a classification of minimal representations of connected simple real lie groups not of type a actually we prove that there exist no new minimal representations up to infinitesimal equivalence

minimal and random generation of permutation and matrix groups we prove explicit bounds on the numbers of elements needed to generate various types of finite permutation groups and finite completely reducible matrix groups and present examples to show that they are sharp in all cases the bounds are linear in the degree of the permutation or matrix group in general and logarithmic when the group is primitive they can be combined with results of lubotzky to produce explicit bounds on the number of random elements required to generate these groups with a specified probability these results have important applications to computational group theory our proofs are inductive and largely theoretical but we use computer calculations to establish the bounds in a number of specific small cases

classification of unitary highest weight representations for noncompact real forms using jakobsen theorems unitarizability in hermitian symmetric spaces is discussed the set of all missing highest weights is explicitly calculated and the construction of their corresponding highest weights vectors is studied

hermitian presentations of chevalley groups ii abstract we give a presentation for a chevalley group arising from a hermitian lie algebra whose roots have all the same length this is a variant of steinberg s presentation of a general chevalley group using only noncompact roots

homogeneous vector bundles and intertwining operators for symmetric domains the main features of homogeneous cowen douglas operators well known for the unit disk are generalised to the setting of hermitian bounded symmetric domains of arbitrary rank c 2016 elsevier inc all rights reserved

lowest weight modules of sp2n r of minimal gelfand kirillov dimension abstract this paper is to classify genuine irreducible lowest weight modules of sp 2 n r of gelfand kirillov dimension n

on the solvability of closest point projection procedures in contact analysis analysis and solution strategy for surfaces of arbitrary geometry abstract the uniqueness and existence of the closest point projection procedure widely used in contact mechanics are analyzed in the current article first a projection domain for c 2 continuous surfaces is created based on the geometrical properties of surfaces then any point from the projection domain has a unique projection onto the given surface it is shown that in order to construct a continuous projection domain for arbitrary globally c 1 or c 0 continuous surfaces a projection routine should be generalized and also include a projection onto a curved edge and onto corner points criteria of uniqueness and existence of the corresponding projection routine are given and discussed from the geometrical point of view some examples showing the construction of the projection domain as well as the necessity of a generalized projection routine are given

theta lifting of unitary lowest weight modules and their associated cycles we consider a reductive dual pair g g in the stable range with g the smaller member and of hermitian symmetric type we study theta lifting of holomorphic nilpotent k c orbits in relation to theta lifting of unitary lowest weight modules of g we determine the associated cycles of all such representations in particular we prove that the multiplicity in the associated cycle is preserved under theta lifting

boundary value maps szego maps and intertwining operators we consider one series of unitarizable representations the cohomological induced modules aq a with dominant regular infinitesimal character the minimal k type ir v of aq a determines a homogeneous vector bundle v g k the derived functor modules can be realized on the solution space of a first order differential operator da on v barchini knapp and zierau gave an explicit integral map s from the derived functor module realized in the langlands classification into the space of smooth sections of the vector bundle v g k in this paper we study the asymptotic behavior of elements in the image of s we obtain a factorization of the standard intertwining opeartors into the composition of the szego map s and a passage to boundary values 0 introduction let g be a linear connected semisimple lie group and let k be a maximal compact subgroup of g we assume that rank g rank k in this situation the cohomologically induced representation aq a with dominant regular infinitesimal character can be realized on solution spaces of invariant differential equations in g k see wo b 2 the minimal k type r v of aq a determines an homogeneous vector bundle vtr g k corresponding to certain choices of positive roots there is defined a certain homogeneous first order differential operator d on vtu in bkz and b 1 the authors gave an explicit nonzero integral map s from the derived functor module realized in the langlands classification to the space of smooth sections of the vector bundle vt g k the image of s is annihilated by the differential operator d when the representation under consideration is in the discrete series of g the differential operator vd coincides with schmid s differential operator s in this case the s transform was introduced by knapp and wallach in kw the realization of irreducible unitary representations in the g k picture generalizes bargmann s formulation of holomorphic discrete series of su 1 1 bar in terms of semisimple lie groups functions on the circle suggest non unitary principal series and holomorphic functions on the disk suggest discrete series representations the s transform in kw reduces in limiting cases limits of discrete series for su 1 1 to the szeg6 kernel for the disk see k 1 thus we call s a szeg6 map received by the editors february 17 1995 and in revised form october 9 1995 1991 mathematics subject classification primary 22c05 22e45 22e46 1997 american mathematical society 1877 this content downloaded from 207 46 13 124 on wed 22 jun 2016 05 42 59 utc all use subject to http about jstor org terms

positive energy representations holomorphic discrete series and finite dimensional irreps let g be a semi simple non compact lie group with unitary lowest highest weight representations we consider explicitly the relation among three types of representations of g positive energy unitary lowest weight representations holomorphic discrete series representations and non unitary finite dimensional irreps we consider mainly the conformal groups soo n 2 treating in full detail the cases n 1 3 4

mortar based frictional contact formulation for higher order interpolations using the moving friction cone abstract finite element discretizations including contact usually apply the standard nts node to segment element thus a coupling with higher order solid elements leads to inconsistencies in the transmission of contact stresses one can circumvent this using the mortar method which includes a weak projection of the contact constraints in this paper we present a penalty formulation based on the mortar concept for two dimensional large deformation frictional contact the discretization of the contact surfaces contains quadratic approximations which can be used within a quadratic approximation of the solid elements to obtain a simple and efficient matrix formulation the moving friction cone algorithm is applied

nilpotent orbits and some small unitary representations of indefinite orthogonal groups abstract for 2 m l 2 let g be a simply connected lie group with g 0 so 2m 2l 2m as lie algebra let g k p be the complexification of the usual cartan decomposition let k be the analytic subgroup with lie algebra k g 0 and let u g be the universal enveloping algebra of g this work examines the unitarity and k spectrum of representations in the analytic continuation of discrete series of g relating these properties to orbits in the nilpotent radical of a certain parabolic subalgebra of g the roots with respect to the usual compact cartan subalgebra are all ei ej with 1 i q l u be the parabolic subalgebra of g for which em em 1 contributes to u and the other simple roots contribute to l let l be the analytic subgroup of g with lie algebra l g 0 let l c int g l let 2 u be the sum of the roots contributing to u and let q l u be the parabolic subalgebra opposite to q the members of u p are nilpotent members of g the group l c acts on u p with finitely many orbits and the topological closure of each orbit is an irreducible algebraic variety if y is one of these varieties let r y be the dual coordinate ring of y this is a quotient of the algebra of symmetric tensors on u p that carries a fully reducible representation of l c for s z let s k 1 m l s 2 e k then s defines a one dimensional l l module c s extend this to a q l module by having u act by 0 and define n s 2 u u g q c s 2 u let n s 2 u be the unique irreducible quotient of n s 2 u the representations under study are s s n s 2 u and s s n s 2 u where s dim u k and s is the sth derived bernstein functor for s 2l 2 it is known that s s and that s is in the discrete series enright parthsarathy wallach and wolf showed for m s 2l 2 that s s and that s is still unitary the present paper shows that s is unitary for 0 s m 1 even though s s and it relates the k spectrum of the representations s to the representation of l c on a suitable r y with y depending on s use of a branching formula of d e littlewood allows one to obtain an explicit multiplicity formula for each k type in s the variety y is indispensable in the proof the chief tools involved are an idea of b gross and wallach a geometric interpretation of littlewood s theorem and some estimates of norms it is shown further that the natural invariant hermitian form on s does not make s unitary for s l c on any r y a final section of the paper treats in similar fashion the simply connected lie group with lie algebra g 0 so 2m 2l 2m 1 2 m l 2

on the role of frame invariance in structural mechanics models at finite rotations in this work we re examine so called geometrically exact models for structures such as beams shells or solids with independent rotation field with respect to invariance under superposed rigid body motion a special attention is given to clarifying the issues pertaining to the finite element implementation which guarantees that the invariance of the continuum problem is preserved by its discrete approximation several numerical simulations dealing with finite rotations of structural models are presented in order to further illustrate and confirm the given theoretical considerations

knapp wallach szegő integrals ii the higher parabolic rank case let g be a connected reductive linear lie group with compact center and real rank 1 for each integer k 1 k 1 and each discrete series representation x of g an explicit embedding of g into a generalized principal series representation induced from a parabolic subgroup of rank k is given the existence of such embeddings was proved by w schmid in this paper an explicit integral formula with szegb kernel is given which provides these mappings

knapp wallach szego integrals and generalized principal series representations the parabolic rank one case abstract to each discrete series representation of a connected semisimple lie group g with finite center a g equivariant embedding into a generalized principal series representation is given this representation is induced from specified parameters on a maximal parabolic subgroup of g and the mapping is defined by an integral formula analogous to the szego integral introduced by knapp and wallach for a minimal parabolic subgroup in a limiting case embeddings of limits of discrete series representations are obtained and used to exhibit a reducibility theorem

cauchy szego maps invariant differential operators and some representations of su n 1 1 on considere des realisations concretes des groupes de lie et en particulier du groupe de lie semi simple su n 1 1

transient three dimensional domain decomposition problems frame indifferent mortar constraints and conserving integration the present work deals with transient large deformation domain decomposition problems the tying of dissimilar meshed grids is performed by applying the mortar method in this connection a reformulation of the original linear mortar constraints is proposed which retains frame indifference for arbitrary discretizations of the interface furthermore a specific coordinate augmentation technique is proposed to make possible the design of an energy momentum scheme numerical examples demonstrate the robustness and enhanced numerical stability of the newly developed energy momentum scheme for three dimensional problems copyright 2009 john wiley sons ltd

a modified node to segment algorithm passing the contact patch test summary several investigations have shown that the classical one pass node to segment nts algorithms for the enforcement of contact constraints fail the contact patch test this implies that the algorithms may introduce solution errors at the contacting surfaces and these errors do not necessarily decrease with mesh refinement the previous research has mainly focused on the lagrange multiplier method to exactly enforce the contact geometry conditions the situation is even worse with the penalty method due to its inherent approximation that yields a solution affected by a non zero penetration the aim of this study is to analyze and improve the contact patch test behavior of the one pass nts algorithm used in conjunction with the penalty method for 2d frictionless contact the paper deals with the case of linear elements for this purpose several sequential modifications of the basic formulation have been considered which yield incremental improvements in results of the contact patch test the final proposed formulation is a modified one pass nts algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method in other words this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration copyright q 2009 john wiley sons ltd

the langlands parameters of subquotients of certain derived functor modules letgbe a noncompact simple lie group with finite center letkbe a maximal compact subgroup and let g0 k0 p0be the corresponding decomposition of the lie algebra suppose rank g rank k and let t0be a compact cartan subalgebra and b be a borel subalgebra letab be a derived functor module with infinitesimal character which is nondominant with respect to a noncompact simple root suppose that 2 p iskdominant so that thektype with highest weight occurs with multiplicity one inab we develop conditions on the roots of g under which a functor of cohomological induction maps a certain module of parabolic induction to another module of parabolic induction extending a result due to vogan this allows us in many cases to determine the langlands parameters of the subquotient ofab containing via a conjectured method of knapp

consistent development of a beam to beam contact algorithm via the curve to solid beam contact analysis for the nonfrictional case summary beam to beam contact can be dually described depending on the scale as contact between curves or contact between surfaces the surface to surface algorithm requires a computationally expensive continuum description of the beams the curve to curve ctc contact algorithm is generated from the corresponding closest point projection cpp procedure determining a minimal distance between curves and involves less expensive beam finite elements the existence and uniqueness criterion of the cpp procedure formulated already in earlier publications is analyzed in detail especially in the case of multiple solutions for parallel curves it is shown that the ctc contact algorithm cannot be applied for general parallel curves which can be generated in an arbitrary range of angles between the tangent lines a new curve to solid beam contact algorithm is here developed this algorithm requires a special solid beam finite element and is combining the advantages of surface contact together with the flexibility of the application to beam to beam contact further a special case with parallel tangent vectors is considered from the classical hertzian contact problem it is found numerically that the corresponding length of a contact zone is well correlated with the hertz theory a possible application of the developed strategy for wire ropes is analyzed numerically this article is protected by copyright all rights reserved

on the uniform spread of almost simple symplectic and orthogonal groups abstract a group is 3 2 generated if every non identity element is contained in a generating pair a conjecture of breuer guralnick and kantor from 2008 asserts that a finite group is 3 2 generated if and only if every proper quotient of the group is cyclic and recent work of guralnick reduces this conjecture to almost simple groups in this paper we prove a stronger form of the conjecture for almost simple symplectic and odd dimensional orthogonal groups more generally we study the uniform spread of these groups obtaining lower bounds and related asymptotics this builds on earlier work of burness and guest who established the conjecture for almost simple linear groups

the center of the quantized matrix algebra abstract we compute the center in the case where q is a root of unity the main steps are to compute the degree of an associated quasipolynomial algebra and to compute the dimensions of some interesting irreducible modules

on finite element implementation of geometrically nonlinear reissner s beam theory three dimensional curved beam elements abstract finite element implementation of the three dimensional finite strain beam theory of reissner is considered in this work in contrast with some earlier works on the subject discussed here are the beam elements whose reference axes are arbitrary space curved lines we have shown that an improved representation of curved reference geometry significantly increases the accuracy of the results however it also makes the choice of non locking finite element interpolations somewhat more delicate a hierarchical displacement interpolation proposed here is proved to be capable of eliminating both shear and membrane locking phenomena a very satisfying non locking performance is demonstrated for a set of problems in nonlinear elasto statics

hilbert series howe duality and branching rules abstract let be a partition with l parts and let f be the irreducible finite dimensional representation of gl m associated to when l m the littlewood restriction rule describes how f decomposes when restricted to the orthogonal group o m or to the symplectic group sp m 2 under the condition that l m 2 in this paper this result is extended to all partitions our method combines resolutions of unitary highest weight modules by generalized verma modules with reciprocity laws from the theory of dual pairs in classical invariant theory corollaries include determination of the gelfand kirillov dimension of any unitary highest weight representation occurring in a dual pair setting and the determination of their hilbert series as a graded module for p let l be a unitary highest weight representation of sp n r so 2n or u p q when the highest weight of l plus satisfies a partial dominance condition called quasi dominance we associate to l a reductive lie algebra gl and a graded finite dimensional representation bl of gl the representation bl will have a hilbert series p q that is a polynomial in q with positive integer coefficients let l be the gelfand kirillov dimension of l and set cl equal to the ratio of the dimensions of the zeroth levels in the gradings of l and bl then the hilbert series of l may be expressed in the form in the easiest example of the correspondence l bl the two components of the weil representation of the symplectic group correspond to the two spin representations of an orthogonal group

recognizing the prime divisors of the index of a proper subgroup abstract let g be a finite group and let c be a subgroup of g we prove that in order to get information on the set of primes dividing the index g c of c in g it is enough to look at the primes dividing h c h where h is a suitable subgroup of g with few generators

unitarizable highest weight modules of the conformal group we give the classification and structure of all untarizable highest weight representations of the group su 2 2 using recent results of m kashiwara r parthasarathy and m vergne we verify a conjecture of kashiwara and vergne that all such representations occur as subrepresentation of the segal shale weil representation and its k fold tensor products in fact k may be taken to be 3 as an application we obtain the complete analytic continuation of the holomorphic discrete series of representations of su 2 2 a result first obtained by k gross and w holman iii by entirely different methods

group representations arising from lorentz conformal geometry abstract it is shown that there exist conformally covariant differential operators d 2 l k of all even orders 2 l on differential forms of all orders k in the double cover n of the n dimensional compactified minkowski space n these act as intertwining differential operators for natural representations of o 2 n the conformal group of n for even n the resulting decompositions of differential form representations of o 2 n the orthochronous conformal group produce infinite families of unitary representations the most interesting of which are carried by positive mass squared positive frequency quotients for 2l n 2k physically these generalize unitary representations of the conformal group associated with the modified wave operator d 2 0 n 2 2 2 and the maxwell operator on vector potentials d 2 n 2 2 d all the representation spaces produced unitary and nonunitary may be viewed as infinite systems of harmonic oscillators as a by product of the spectral resolution of the d 2 l k one gets some striking wave propagative properties for all of the equations d 2 l k 0 including huygens principle in the curved spacetime n the operators d 2 l k have not been seen before except in the special cases k 0 or n and k n 2 2 l 1 the maxwell operator thus much new information is obtained even in the physical case n 4

on some aspects for contact with rigid surfaces surface to rigid surface and curves to rigid surface algorithms abstract special algorithms allowing a simplified description of contact between deformable body and rigid surfaces are developed based on the geometrically exact covariant description of contact a special attention is given to various geometric combinations where the contact can be represented as a contact between surfaces and b contact between a curve and a surface for contact between surfaces leading to the segment to analytical surface stas approach two algorithms can be distinguished based on the selection of a coordinate system for the closest point projection cpp procedure a rigid surface is a slave surface and b rigid surface is a master surface a special combination of both contact kinematics for the surface to surface and for the curve to curve approaches is employed for the contact between a curve and a surface leading to the curve to rigid surface ctrs approach the last algorithm is verified with the well known euler formula for the rope cylinder interaction as well as with a new derived generalization into a 3d spiral rope on a cylinder the developed algorithms can be straightforwardly implemented within an iso geometric approach as well as within the conventional finite elements where rigid surfaces are given by cad patches any type of elements can be employed for the contacting deformable surface curve because the algorithms are formulated in a covariant form

quantization of the action of u k l on r2 k l abstract the natural action of u k l on c k l leaves invariant a real skew non degenerate bilinear form b which turns c k l into a symplectic manifold m the polarization f of m defined by the complex structure of c k l is non positive if l is the prequantization complex line bundle carried by m then u k l acts on the space u of square integrable l f forms on m leaving invariant the natural non degenerate but non definite inner product on u the polarization f also defines a closed densely defined covariant differential on u which is u k l invariant let denote orthocomplementation with respect to it is shown that the restriction of to the u k l stable subspace ker im is semi definite and that the unitary representation of uk l on the hilbert space h arising from by dividing out null vectors is unitarily equivalent to the representation of u k l obtained from the tensor product of the metap ectic and det 1 2 representations of mu k l the double cover of u k l

boundary value problems for various boundaries of hermitian symmetric spaces abstract the image of the poisson transform on a principal series representations on a boundary component of a hermitian symmetric space is considered we prove that the image is characterized by a covariant differential operator on a homogeneous line bundle on the symmetric space

singular unitary representations and indefinite harmonic theory abstract square integrable harmonic spaces are defined and studied in a homogeneous indefinite metric setting in the process dolbeault cohomologies are unitarized and singlar unitary representations are obtained and studied

hermitian symmetric spaces and their unitary highest weight modules abstract the purpose of this article is to determine the set of unitarizable highest weight modules corresponding to hermitian symmetric spaces of the noncompact type the major step is that of proving unitarity at the last possible place with this established the description of the full set of unitarizable highest weight modules follows by a straightforward tensor product argument combined with the main ingredients of the proof of the key theorem bernstein gelfand gelfand and a diagramatic representation of the set of positive noncompact roots

finite groups with a large automorphism orbit abstract we study the nonabelian composition factors of a finite group g assumed to admit an aut g orbit of length at least g for a given 0 1 our main results are the following the orders of the nonabelian composition factors of g are then bounded in terms of and if 18 19 then g is solvable on the other hand for each nonabelian finite simple group s there is a constant c s 0 1 such that s occurs with arbitrarily large multiplicity as a composition factor in some finite group g having an aut g orbit of length at least c s g

gradient type differential operators and unitary highest weight representations of su p q abstract let c p q be equipped with a hermitian form of signature p q and let su p q denote the subgroup of the corresponding invariance group u p q consisting of matrices with determinant 1 to certain highest weights we associate a first order group invariant linear differential operator d whose kernel contains a unitary highest weight representation with highest weight the fock model realization of unitary highest weight representations of u p q is the fundamental tool used to implement this construction the operator d is shown to be equivalent to an operator d which acts on hol g k h the space of holomorphic vector valued functions defined on g k we identify a set 1 of highest weights such that ker d is a proper subspace of hol g k h and show that those in 1 correspond to points occurring at the far right of the discrete set in the classification scheme of enright howe and wallach first order differential equations arising from this proper containment are explicitly derived from the operator d we illustrate the fundamental nature of these first order equations by deriving from them a system which completely determines the irreducible spaces for ladder representations of su p q

maximal subgroups in finite and profinite groups we prove that if a finitely generated profinite group g is not generated with positive probability by finitely many random elements then every finite group f is obtained as a quotient of an open subgroup of g the proof involves the study of maximal subgroups of profinite groups as well as techniques from finite permutation groups and finite chevalley groups confirming a conjecture from ann of math 137 1993 203 220 we then prove that a finite group g has at most igic maximal soluble subgroups and show that this result is rather useful in various enumeration problems

three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs a three dimensional mortar based frictional contact treatment in isogeometric analysis with nurbs is presented in the finite deformation regime within a setting where the nurbs discretization of the contact surface is inherited directly from the nurbs discretization of the volume the contact integrals are evaluated through a mortar approach where the geometrical and frictional contact constraints are treated through a projection to control point quantities the formulation delivers a non negative pressure distribution and minimally oscillatory local contact interactions with respect to alternative lagrange discretizations independent of the discretization order these enable the achievement of improved smoothness in global contact forces and moments through higher order geometrical descriptions it is concluded that the presented mortar based approach serves as a common basis for treating isogeometric contact problems with varying orders of discretization throughout the contact surface and the volume

covariant q differential operators and unitary highest weight representations for u q su n n we investigate a one parameter family of quantum harish chandra modules of uqsl2n this family is an analog of the holomorphic discrete series of representations of the group su n n for the quantum group uqsun n we introduce a q analog of the wave operator a determinant type differential operator and prove certain covariance property of its powers this result is applied to the study of some quotients of the above mentioned quantum harish chandra modules we also prove an analog of a known result by j faraut and a koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series

unitary highest weight modules the unitary highest weight modules of a semisimple lie group g have been classified s 93 unfortunately this classification does not fit well with a more general picture of the unitary dual of g we give such a classification for g a classical group using derived functors and the philosophy of unipotent representations in particular these representations are associated to coadjoint orbits of g let 8 lie g 0 a cartan involution of 6 8 c a derived functor module is defined by the data q i u a o stable parabolic subalgebra of 0 and 17 an irreducible unitary representation of l the stabilizer of l in g considering z7 as a representation of i write z7 a rc where a e c c center of i denotes dual and rt z7l r we define a rc i rc cf definition 6 1 now fix n and vary 1 under certain restrictions on i which amount to a positivity condition on the corresponding bundle over g l a i rr is known to be irreducible and unitary as ii varies within this range the langlands parameters of a a rr vary smoothly however one cannot obtain all unitary highest weight modules under these restrictions the orbit method suggests how to obtain the remaining unitary highest weight modules the modules a rr are associated to coadjoint orbits as follows if rc is trivial we say a rr is associated to the elliptic orbit 0 g ii not all unitary highest weight modules may be obtained with rc trivial an example of which is the oscillator representation of 2n r the metapletic group we define 2n irreducible unitary highest weight modules rc 1 2 n k r is 113 oool 8708 87 7 50

minimal generation of transitive permutation groups this thesis discusses upper bounds on the minimal number of elements d g required to generate a finite group g we derive explicit upper bounds for the function d on transitive and minimally transitive permutation groups in terms of their degree n in the transitive case bounds obtained first by kovacs and newman then by bryant kovacs and robinson and finally by lucchini menegazzo and morigi show that d g o n log n for a transitive permutation group g of degree n in this thesis we find best possible estimates for the constant involved please consult thesis for remaining section of abstract

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

consistent mesh tying methods for topologically distinct discretized surfaces in non linear solid mechanics this work presents a new technique for joining dissimilar meshes in non linear finite element analysis with the novel result that the adjoining surfaces do not need to be spatially coincident for patch tests to be passed the work builds in some sense on results previously presented by dohrmann et al international journal for numerical methods in engineering 1991 40 1205 but considerably generalizes upon the results presented there most importantly it is shown that consistency of the tied finite element formulation may be achieved such that implementation of element formulations is not affected through the use of a three field variational principle applied over the contacting region a key conclusion of the work is that although the approach advocated bears some resemblance to mortar element schemes for contact analysis see for example mcdevitt and laursen international journal for numerical methods in engineering 2000 48 1525 a straightforward application of a mortaring scheme is not sufficient to guarantee patch test passage when dissimilar meshing of curved surfaces leads to local open volumes or overlaps between tied surfaces in their reference configurations the proposed algorithm is demonstrated through a number of numerical examples performed within a matrix free non linear equation solving framework published in 2003 by john wiley sons ltd

an cohomology construction of unitary highest weight modules for in this paper a geometric construction is given of all unitary highest weight modules of g u p q the construction is based on the unitary model of the kth tensor power of the metaplectic representation in a bargmannsegal fock space of square integrable differential forms the representations are constructed as holomorphic sections of certain vector bundles over g k and the construction is implemented via an integral transform analogous to the penrose transform of mathematical physics 0 introduction a major area of research in the representation theory of lie groups is the explicit analysis of naturally occurring unitary representations one aspect of this problem is that of producing geometric constructions of the unitary representations of a semisimple lie group g here we consider unitary highest weight representations of g u p q these representations have been classified algebraically in various ways see ehw j1 a and have been constructed as spaces of vector valued functions on the generalized unit disk d ds most singular highest weight representations appear in the l 2 cohomology construction of rsw z our approach starts with the kth tensor power of the metaplectic representation of u p q in the l cohomology space zo k cnxk as defined by blattner and rawnsley br the reductive dual pair u p q u k acts on this space results of kashiwara and vergne kv decompose this space into a sum of irreducible representations ua indexed by a set a c u k of representations of u k all unitary highest weight modules of u p q appear in this way for some k j2 ep each irreducible g u p q module corresponds to a vector bundle over g k as follows corresponding to a particular representation a of g each element c of g k determines a subspace vs c received by the editors october 31 1989 results presented in the special session on geometric methods in representation theory at the american mathematical society meeting in los angeles califormia november 1987 1980 mathematics subject classification 1985 revision primary 22e45

on induced scalar products and unitarization infinitesimal unitarity of representations of the simple real lie algebras su 2 su 1 1 and so 4 is discussed with respect to scalar products induced by sesquilinear forms on their universal enveloping algebras sesquilinear forms are explicitly calculated the verma modules their irreducible quotients their irreducible submodules and their infinitesimal unitarizability are discussed

geometrically exact theory for contact interactions of 1d manifolds algorithmic implementation with various finite element models abstract the intuitive understanding of contact between bodies is based on the geometry of adjoining bodies a more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system the best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies this leads to a systematical analysis of geometrical situations leading to contact pairs surface to surface line to surface point to surface line to line point to line each contact pair is inherited with a special coordinate system based on its geometrical properties the current contribution is concentrating on contact between 1d manifolds in 3d space this is the majority of edge to edge beam to beam cable to edge etc contact cases the geometrically exact curve to curve contact approach is then systematically combined together with various finite element approaches classical finite elements isogeometric beam finite elements and also with a new developed solid beam approach examples illustrating the diversity of various finite element combinations e g within knot mechanics are shown

a new class of unitarizable highest weight representations of infinite dimensional lie algebras ii on donne les details rigoureux pour le probleme de classification on redemontre l unitarite de la representation exceptionnelle on considere les produits tensoriels et les problemes d integrabilite

generalized kepler problems i without magnetic charges for each simple euclidean jordan algebra v of rank and degree we introduce a family of classical dynamic problems these dynamical problems all share the characteristic features of the kepler problem for planetary motions such as the existence of laplace runge lenz vector and hidden symmetry after suitable quantizations a family of quantum dynamic problems parametrized by the nontrivial wallach parameter is obtained here w v k 2 k 1 1 1 2 and was introduced by n wallach to parametrize the set of nontrivial scalar type unitary lowest weight representations of the conformal group of v for the quantum dynamic problem labelled by the bound state spectra is 1 2 i 2 2 i 0 1 and its hilbert space of bound states gives a new realization for the afore mentioned representation labelled by a few results in the literature about these representations become more explicit and more refined the lagrangian for a classical kepler type dynamic problem introduced here is

hilbert series howe duality and branching for classical groups an extension of the littlewood restriction rule is given that covers all pertinent parameters and simplifies to the original under littlewood s hypotheses two formulas are derived for the gelfand kirillov dimension of any unitary highest weight representation occurring in a dual pair setting one in terms of the dual pair index and the other in terms of the highest weight for a fixed dual pair setting all the irreducible highest weight representations which occur have the same gelfand kirillov dimension we define a class of unitary highest weight representations and show that each of these representations l has a hilbert series hl q of the form

unitary structures on cohomology let cp 4 be endowed with a hermitian form h of signature p q let m be the manifold of r dimensional subspaces of cp p q on which h is positive defi nite and let e be the determinant bundle of the tautological bundle on mr we show starting from the oscillator representation of su p q that there is an invariant subspace of hr p r mr 9 e p k which defines a unitary representation of su p q for w ei mp gr r w is the subvariety of r dimensional subspaces of w integration over gr r w associates to an r p r cohomology class a a function p a on mp we show that this map is injective and provides an intertwin ing operator with representations of su p q on spaces of holomorphic functions on siegel space

a mixed formulation of mortar based frictionless contact abstract a class of mortar based frictionless contact formulations is derived based on a classical three field mixed variational framework within a penalty regularization complemented by uzawa augmentations discrete mortar constraints are naturally induced by the variational setting major aspects of earlier mortar approaches are obtained through constrained lumped or unconstrained recovery procedures for the mixed kinematic and kinetic mortar quantities from their projected counterparts two and three dimensional examples at the infinitesimal and finite deformation regimes highlight the local and global quality of the contact interactions

on the choice of finite rotation parameters in this work we discuss some aspects of the three dimensional finite rotations pertinent to the formulation and computational treatment of the geometrically exact structural theories among various possibilities to parameterize the finite rotations special attention is dedicated to a choice featuring an incremental rotation vector some computational aspects pertinent to the implementation of the newton iterative scheme and the newmark time stepping algorithm applied to solving these problems are examined representative numerical simulations are presented in order to illustrate the performance of the proposed formulation

unitary positive energy representations of scalar bilocal quantum fields the superselection sectors of two classes of scalar bilocal quantum fields in d 4 dimensions are explicitly determined by working out the constraints imposed by unitarity the resulting classification in terms of the dual of the respective gauge groups u n and o n confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory but the approach using standard lie algebra methods rather than abstract duality theory is complementary the result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension d 2 in models with global conformal invariance another remarkable outcome is the observation that with an appropriate choice of the hamiltonian a lie algebra embedded into the associative algebra of observables completely fixes the representation theory

an l2 cohomology construction of negative spin mass zero equations for u p q abstract in this paper a geometric construction is given of the ladder representations of g u p q which correspond to negative spin solutions of the massless field equations the construction is based on the unitary model of the ladder representations in a bargmann segal fock space of square integrable 0 q forms the representations are constructed as holomorphic sections of certain vector bundles over g k and the construction is implemented via an integral transform analogous to the penrose transform of mathematical physics finally the resulting differential equations are exhibited explicitly over g k