representations of the symmetric group are reducible over simply transitive subgroups if the characteristic of f is zero this problem has been solved by saxl 16 an important feature of saxl s result is that a groupg as in the problem above is either 2 transitive or fixes a point i e is contained in some n 1 the caseg n 1 can then be settled using the branching rule and induction on the other hand an explicit list of k transitive groups for k 2 is available which can be used to complete the proof in characteristic zero see 16 for more details from now on we assume that p 0 in this case the problem is important for determining maximal subgroups of finite classical groups 1 13 however the situation is nowmore complicated for example to determine the pairs g d as above withg an one needs the mullineux conjecture 7 2 ifg is intransitive then up to a conjugation it is contained in a standard young subgroup of the form n k k the irreducible restrictions from n to n 1 have been described in 14 see also 11 6 in 11 it is also

non convergence of formal integrals of motion we consider formal integrals of motion in 2d hamiltonian dynamical systems calculated with the normal form method of giorgilli 1979 comput phys commun 16 331 three different non integrable and one integrable systems are considered the time variation di of the formal integral i is found as a function of the order of truncation n of the integral series an optimal order of truncation is found from the minima of the variations di the level lines of the integral i representing theoretical invariant curves on a poincare surface of section are compared with the real invariant curves when chaos is limited excellent agreement is found between the theoretical and the real invariant curves if the order of truncation is close to the optimal order the agreement is poor a far from the optimal order and b when chaos is pronounced the optimal order calculated as a function of the distance r from the origin decreases when r increases the decrease is rather smooth in the 1 1 resonance but it has abrupt steps in the case of a higher order 4 3 resonance in the case of an integrable hamiltonian a formal integral if is found which is a function of the exact integral i and of the hamiltonian given as power series of the canonical variables the series converges only within a domain of convergence the radius of convergence along a particular direction is calculated with the d alembert and cauchy methods the theoretical invariant curves agree with the real invariant curves only within the domain of convergence of if in the case of non integrable hamiltonians we calculate pseudo radii of convergence that tend to zero as the order of truncation n increases

a parametric level set approach to simultaneous object identification and background reconstruction for dual energy computed tomography dual energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography the purpose of this paper is to introduce a novel polychromatic dual energy processing algorithm with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown cluttered background physical properties of the objects particularly the compton scattering and photoelectric absorption coefficients are assumed to be known with some level of uncertainty our approach is based on a level set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object and the fundamental physics based limitations associated with our ability to jointly recover the compton scattering and photoelectric absorption properties of the scene in the absence of an object with appropriate physical properties our approach returns a null characteristic function and thus can be viewed as simultaneously solving the detection and characterization problems unlike the vast majority of methods that define the level set function nonparametrically i e as a dense set of pixel values we define our level set parametrically via radial basis functions and employ a gauss newton type algorithm for cost minimization numerical results show that the algorithm successfully detects objects of interest finds their shape and location and gives an adequate reconstruction of the background

multiplicity free subgroups of reductive algebraic groups abstract we introduce the notion of a multiplicity free subgroup of a reductive algebraic group in arbitrary characteristic this concept already exists in the work of kramer for compact connected lie groups we give a classification of reductive multiplicity free subgroups and as a consequence obtain a simple proof of a theorem of kleshchev

spherical conjugacy classes and involutions in the weyl group let g be a simple algebraic group over an algebraically closed field of characteristic zero or positive odd good characteristic let b be a borel subgroup of g we show that the spherical conjugacy classes of g intersect only the double cosets of b in g corresponding to involutions in the weyl group of g this result is used in order to prove that for a spherical conjugacy class mathcal o with dense b orbit v0 bwb there holds ell w rm rk 1 w dim mathcal o extending to the case of groups over fields of odd good characteristic a characterization of spherical conjugacy classes obtained by cantarini costantini and the author it is also shown that the weights occurring in the g module decomposition of the ring of regular functions on mathcal o are self adjoint and they lie in the 1 eigenspace of the element w

maximal ideals in modular group algebras of the finitary symmetric and alternating groups the main result of the paper is a description of the maximal ideals in the modular group algebras of the finitary symmetric and alternating groups provided the characteristic p of the ground field is greater than 2 for the symmetric group there are exactly p 1 such ideals and for the alternating group there are p 1 2 of them the description is obtained in terms of the annihilators of certain systems of the completely splittable irreducible modular representations of the finite symmetric and alternating groups the main tools used in the proofs are the modular branching rules obtained earlier by the second author and the mullineux conjecture proved recently by fordkleshchev and bessenrodt olsson the results obtained are relevant to the theory of pi algebras they are used in a later paper by the authors and a e zalesskii on almost simple group algebras and asymptotic properties of modular representations of symmetric groups

edge preserving tomographic reconstruction with nonlocal regularization tomographic image reconstruction using statistical methods can provide more accurate system modeling statistical models and physical constraints than the conventional filtered backprojection fbp method because of the ill posedness of the reconstruction problem a roughness penalty is often imposed on the solution to control noise to avoid smoothing of edges which are important image attributes various edge preserving regularization methods have been proposed most of these schemes rely on information from local neighborhoods to determine the presence of edges in this paper we propose a cost function that incorporates nonlocal boundary information into the regularization method we use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function jointly estimating region boundaries and object pixel values we apply variational techniques implemented using level sets methods to update the boundary estimates then using the most recent boundary estimate we minimize a space variant quadratic cost function to update the image estimate for the positron emission tomography transmission reconstruction application we compare the bias variance tradeoff of this method with that of a conventional penalized likelihood algorithm with local huber roughness penalty

isomorphisms between simple modules of degenerate cyclotomic hecke algebras abstract we give explicit isomorphisms between simple modules of degenerate cyclotomic hecke algebras defined via various cellular bases a special case gives a generalized mullineux involution in the degenerate case

nonconvergence of formal integrals ii improved estimates for the optimal order of truncation we investigate the asymptotic properties of formal integral series in the neighbourhood of an elliptic equilibrium in nonlinear 2 dof hamiltonian systems in particular we study the dependence of the optimal order of truncation nopt on the distance from the elliptic equilibrium by numerical and analytical means the function nopt determines the region of nekhoroshev stability of the orbits and the time of practical stability we find that the function nopt decreases by abrupt steps the decrease is roughly approximated with an average power law nopt o a with a 1 we find an analytical explanation of this behaviour by investigating the accumulation of small divisors in both the normal form algorithm via lie series and in the direct construction of first integrals precisely we find that the series exhibit an apparent radius of convergence that tends to zero by abrupt steps as the order of the series tends to infinity our results agree with those obtained by servizi g et al 1983 phys lett a 95 11 for a conservative map of the plane moreover our analytical considerations allow us to explain the results of our previous paper contopoulos g et al 2003 j phys a math gen 36 8639 including in particular the different behaviour observed for low order and higher order resonances

irreducible restrictions of representations of symmetric and alternating groups in small characteristics abstract building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups such a classification is known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas our results fit into the aschbacher scott program on maximal subgroups of finite classical groups

an energy momentum map for the time reversal symmetric 1 1 resonance with z 2 z 2 symmetry abstract we present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1 1 resonant hamiltonian normal forms invariant under z 2 z 2 symmetry the rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods the geometric approach readily allows to find an energy momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features quadrature formulas for the actions periods and rotation number are also provided

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

dynamic multi source x ray tomography using a spacetime level set method a novel variant of the level set method is introduced for dynamic x ray tomography the target is allowed to change in time while being imaged by one or several source detector pairs at a relatively high frame rate the algorithmic approach is motivated by the results in 22 showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography furthermore defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here the tomographic reconstruction is found as a minimizer of a nonlinear functional the functional contains a regularization term penalizing the l 2 norms of up to n derivatives of the reconstruction the case n 1 is shown to be equivalent to a convex tikhonov problem that has a unique minimizer for n 2 the existence of a minimizer is proved under certain assumptions on the signal to noise ratio and the size of the regularization parameter numerical examples with both simulated and measured dynamic x ray data are included and the proposed method is found to yield reconstructions superior to standard methods such as fbp or non negativity constrained tikhonov regularization and favorably comparable to those of total variation regularization furthermore the methodology can be adapted to a wide range of measurement arrangements with one or more x ray sources

asymptotic results on modular representations of symmetric groups and almost simple modular group algebras in fact this is a question about infinite simple groups because it is easy for g finite and because a non trivial normal subgroup gives rise to a non trivial ideal different from the augmentation ideal also note that the problem reduces easily to the question on when the augmentation ideal is simple as a ring the first interesting class of groups with almost simple fg was discovered in 3 this class is rather exotic and contains groups like the universal hall group and algebraically closed groups for locally finite groups g a substantial progress was achieved recently by using representation theory of finite groups see 18 19 16 and others the representation theory approach transforms the problems on ideals to certain problems on asymptotic behavior of representations of finite groups which are often of independent interest the method is more effective over fields of characteristic zero as the theory of ordinary representations is much better elaborated than the modular theory this paper is devoted to the modular aspect of the theory one of our main results deals with the case where g is a direct limit of alternating groups and f is any field of characteristic p 2 we note that the case where charf 0 was considered in 18 let n be the set of natural numbers denote by alt and sym or simply an and n the alternating and symmetric groups respectively on a set with n let alt 1 alt 2 alt i 1

limited data x ray tomography using nonlinear evolution equations a novel approach to the x ray tomography problem with sparse projection data is proposed nonnegativity of the x ray attenuation coefficient is enforced by modelling it as max phi x 0 where phi is a smooth function the function phi is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods the reconstruction algorithm is applied to a simulated full and limited angle projection data of the shepp logan phantom with sparse angular sampling and b measured limited angle projection data of in vitro dental specimens the results are significantly better than those given by traditional backprojection based approaches and similar in quality but faster to compute compared to the algebraic reconstruction technique

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

composition factors of tensor products of truncated symmetric powers let g be the general linear group of degree n over an algebraically closed field k of characteristic p 0 we study the m fold tensor product s e m of the truncated symmetric algebra s e of the symmetric algebra s e of the natural module e for g we are particularly interested in the set of partitions occurring as the highest weight of a composition factor of s e m we explain how the determination of these composition factors is related to the determination of the set of composition factors of the m fold tensor product s e m of the symmetric algebra we give a complete description of the composition factors of s e m in terms of distinguished partitions our main interest is in the classical case but since the quantised version is essentially no more difficult we express our results in the general context throughout

rectangular low level case of modular branching problem for gln k abstract in this paper we find an explicit combinatorial criterion for the existence of a nonzero gl n 1 k high weight vector of weight 1 i 1 i d i 1 n 1 where d char k and k is an algebraically closed field in the irreducible rational gl n k module l n 1 n with highest weight 1 n for this purpose new modular lowering operators are introduced

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

a proof of the mullineux conjecture a partition of a positive integer n is a sequence 1 2 m 0 of integers such that i n for a positive integer p a partition 1 2 m or its young diagram is called p regular if it does not have p or more equal parts i e if there does not exist t m p 1 with t t 1 t p 1 let f be a field of characteristic p 0 it is well known that irreducible representations of the symmetric group sn over f are naturally parametrized by pregular partitions of n cf for example 9 12 if is such a partition we denote the corresponding irreducible module by d let sgnn be the one dimensional sign representation of sn over f i e sgnn f as a vector space and g f sgn g f for any g sn f f here sgn g is just the sign of the permutation g it is clear that for any irreducible d the tensor product d sgnn is also irreducible the problem usually called the problem of mullineux is to find the p regular partition such that d sgnn d put d sgnn dn in this way a bijection bn on the set pn of p regular partitions of n is defined for each positive integer n and the problem is

on the role of high order resonances in normal forms and in separatrix splitting we discuss the role of high order resonances in the construction of normal forms for e close to integrable hamiltonian systems by heuristic considerations based on standard estimates we show that the remainder of normal forms is dominated by the terms corresponding to the main high order resonances and we provide a general argument to show that the size of such leading terms is exponentially small in 1e we apply this method to the problem of estimating the splitting of separatrices in resonant perturbed systems

modular branching rules and the mullineux map for hecke algebras of type a in a series of papers 21 22 23 kleshchev has recently proved a branching rule for modular representations of the symmetric group s r on r symbols fix a field f of arbitrary characteristic p then kleshchev s branching rule gives a precise description of the socle of the restriction of an irreducible fs r module to fs r 1 in 24 kleshchev applies this branching rule to give a purely combinatorial description of the mullineux map which describes the irreducible fs r module obtained by tensoring an arbitrary irreducible fs r module with the 1 dimensional sign representation in 13 see also 3 ford and kleshchev show with some technical combinatorics that kleshchev s description of the mullineux map is equivalent to a quite different algorithm conjectured by mullineux 27 in 1979 thus proving the so called mullineux conjecture the main purpose of this paper is to prove the quantum analogues of these results replacing the group algebra fs r with the corresponding hecke algebra h r over f at an arbitrary root of unity q f our main result is the hecke algebra analogue of kleshchev s modular branching rule it turns out that the branching rule for h r only depends on the integer where is the smallest natural number such that 1 q q 1 0 in f if q 1 is precisely the characteristic p of f and our branching rule specializes to the classical case considered by kleshchev as a consequence of this branching rule combining kleshchev s argument in 24 with the known block structure of h r from 9 we are able to deduce the quantum analogue of kleshchev s description of the corresponding mullineux map for h r the proof by ford and kleshchev in 13 that this is equivalent to mullineux s original algorithm does not depend on p being prime so our result is equivalent by 13 to a quantum version of the mullineux conjecture replacing p by we remark that there is now a quite different proof that kleshchev s algorithm gives the mullineux map using crystal bases this was first observed for fields of characteristic 0 in 25 modulo a conjecture which has now been proved 17 2 relating crystal bases for a certain affine quantum group to decomposition matrices of h r over fields of characteristic 0 the result in arbitrary characteristic can be deduced from the characteristic 0 case by an

extensions for finite chevalley groups i let g be a connected semisimple algebraic group defined and split over the field fp with p elements and k be the algebraic closure of fp assume further that g is almost simple and simply connected and let g fq be the finite chevalley group consisting of fq rational points of g where q pr for a non negative integer r in this paper formulas are found relating extensions between simple kg fq modules and extensions over g considered as an algebraic group over k one of these formulas which only holds for primes p 3 h 1 where h is the coxeter number of g is then used to show the vanishing of self extensions between simple kg fq modules except for certain simple modules when r 1 and the underlying root system is of type a1 or cn

irreducible tensor products over alternating groups abstract we classify irreducible tensor products of modular representations of the alternating group over an algebraically closed field of characteristic p 5

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

chirikov and nekhoroshev diffusion estimates bridging the two sides of the river abstract we present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear hamiltonian systems that can be obtained using the heuristic theory of chirikov and a more formal one due to nekhoroshev we show that despite a wide spread impression the two theories are complementary rather than antagonist indeed although chirikov s 1979 review has thousands of citations almost all of them refer to topics such as the resonance overlap criterion fast diffusion the standard or whisker map and not to the constructive theory providing a formula to measure diffusion along a single resonance however as will be demonstrated explicitly below chirikov s formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones provided that it is implemented on the so called optimal normal form derived as in the analytic part of nekhoroshev s theorem on the other hand chirikov s formula yields unrealistic values of the diffusion coefficient in particular for very small values of the perturbation when used in the original hamiltonian instead of the optimal normal form in the present paper we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3dof nearly integrable hamiltonian system besides we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter showing a very satisfactory agreement

representations of the symmetric group which are irreducible over subgroups let f be an algebraically closed field of characteristic p and n be the symmetric group on n letters in this paper we classify all pairs g d where d is an irreducible f n module of dimension greater than 1 and g is a proper subgroup of n such that the restriction d g is irreducible provided p 3

irreducible restrictions of representations of symmetric groups in small characteristics reduction theorems we study irreducible restrictions of modules over symmetric groups to subgroups we get reduction results which substantially restrict the classes of subgroups and modules for which this is possible such results are known when the characteristic of the ground field is greater than 3 but the small characteristics cases require a substantially more delicate analysis and new ideas this work fits into the aschbacher scott program on maximal subgroups of finite classical groups

a characteristic condition for convergence of steepest descent approximation to accretive operator equations in the present paper a sufficient and necessary condition for convergence of steepest descent approximation to accretive operator equations is established and for the sufficiency part a specific error estimation is also given

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

sheaf cohomology on gb and tensor products of weyl modulus let k be an algebraically closed field it is assumed that char k p 0 unless otherwise indicated g is a simply connected semisimple algebraic group over k t is a fixed maximal torus and b a bore1 subgroup of g containing t let qi g t be the root system of g d the set of all simple roots and and the sets of all positive and negative roots relative to d respectively we assume that the set a is chosen such that b corresponds to 0 let x be the weight lattice of sp which may be considered as the character group of t or b therefore if 1 e x by abuse of notation we also denote by l the one dimensional tor b module determined by a let x be the set of all dominant weights and w the fundamental weight corresponding to a simple root a e a we denote by 6 the half sum of all positive roots and we know that 6 is the sum of all fundamental weights let w be the weyl group of 0 the reflection with respect to a root a is denoted by s the longest element of w by w there are two ways of w acting on x i the ordinary action if 1 e x m e w the image of i under w is denoted by 2 ii dot action w a 5 2 6 s in particular let a w a the dual root system of is denoted by and the dual root of a e by a i e u 2a a u where is the inner product invariant under the ordinary action of w of the euclidean space spanned by for 1 e x a e let a a 1 a all modules of an algebraic group we consider in this paper are assumed to be rational in particular for an infinite dimensional module the term rational module means this module is a direct limit of finite dimensional rational modules let h be a closed subgroup of g containing t such as g b or t m an h module we define for l e x

representations of finite special linear groups in non defining characteristic we classify irreducible modules over the finite special linear group sln q in the non defining characteristic l describe restrictions of irreducible modules from gln q to sln q classify complex irreducible characters of sln q irreducible modulo l and discuss unitriangularity of the l decomposition matrix for sln q

double coset density in classical algebraic groups we classify all pairs of reductive maximal connected subgroups of a classical algebraic group g that have a dense double coset in g using this we show that for an arbitrary pair h k of reductive subgroups of a reductive group g satisfying a certain mild technical condition there is a dense h k double coset in g precisely when g hk is a factorization

restriction of irreducible modules for spin 2n 1 k to spin 2n k abstract let k be an algebraically closed field of characteristic p 0 and let y spin 2 n 1 k n 3 be a simply connected simple algebraic group of type b n over k also let x be the subgroup of type d n embedded in y in the usual way as the derived subgroup of the stabilizer of a non singular one dimensional subspace of the natural module for y in this paper we give a complete set of isomorphism classes of finite dimensional irreducible rational ky modules on which x acts with exactly two composition factors completing the work of ford in 12

birkhoff gustavson normal form in classical and quantum mechanics a quantum analogue of the classical transformations to the birkhoff gustavson normal form is derived with unitary transformations taking over the role of canonical transformations the author finds a striking similarity to lie transformations in the classical case the author suggests that the quantum normal form is identical to the rayleigh schrodinger perturbation series and thus usually only asymptotic to the eigenvalues the convergence question of both classical and quantum normal forms is discussed in some detail

on schur algebras and related algebras ii this paper is a continuation of 7 the purpose of 7 was to set up in the context of reductive algebraic groups a theory of generalized schur algebras a special case of our construction gives the schur algebras s n r studied extensively in lo we concentrate here on the schur algebras themselves and show that our construction yields new results in their representation theory by means of the schur functor see 10 chap 6 we obtain new results in the representation theory of the symmetric groups the main results are as follows the schur algebras s n r defined over a principal ideal domain r have finite global dimension see also 1 i over a field or complete valuation ring r every finitely generated projective s n r module has a weyl module filtration we prove the irreducibility of the socle of certain weyl modules see also 15 we describe a connection between weights of projective indecomposable modules for the schur algebras in terms of the involution on irreducible representations of symmetric groups given by tensoring with the sign representation we show that over a complete valuation ring or a field every young module for a symmetric group has a specht series in particular the projective indecomposables have specht series finally we show that for r n and a complete valuation ring or field r the blocks of the schur algebra s n r are given by the rule embodied in nakayama s conjecture the notations and conventions are as in the first part of this work 7

on p blocks of symmetric and alternating groups with all irreducible brauer characters of prime power degree abstract we classify all p blocks of the symmetric and alternating groups where all irreducible p brauer characters are of prime power degree as well as the p blocks of these groups where all p brauer characters are of p power degree this is an extension and a block refinement of an earlier result where all irreducible p brauer characters were assumed to be of p power degree

algebraic reconstruction in ct from limited views the author presents an algebraic reconstruction technique art as a viable alternative in computerized tomography ct from limited views recently algorithms of iterative reconstruction reprojection irr based on the method of convolution backprojection have been proposed for application in limited view ct reprojection was used in an iterative fashion alternating with backprojection as a means of estimating projection values within the sector of missing views in algebraic methods of reconstruction for ct only those projections corresponding to known data are required reprojection along missing views would merely serve to introduce redundant equations computer simulation studies are presented which demonstrate significantly improved reconstructed images achieved by an art algorithm as compared to irr methods

branching of modular representations of the alternating groups abstract based on kleshchev s branching theorems for the p modular irreducible representations of the symmetric group and on the recent proof of the mullineux conjecture we investigate in this article the corresponding branching problem for the p modular irreducible representations of the alternating group a n we obtain information on the socle of the restrictions of such a n representations to a n 1 as well as on the multiplicities of certain composition factors furthermore irreducible a n representations with irreducible restrictions to a n 1 are studied

representations of the general linear groups which are irreducible over subgroups we classify all triples g v h such that sl n q leq g leq gl n q v is a representation of g of dimension greater than one over an algebraically closed field bbb f of characteristic prime to q and h is a proper subgroup of g such that the restriction v downarrow h is irreducible this problem is a natural part of the aschbacher scott program on maximal subgroups in finite classical groups

energy localization on q tori long term stability and the interpretation of fermi pasta ulam recurrences we focus on two approaches that have been proposed in recent years for the explanation of the so called fermi pasta ulam fpu paradox i e the persistence of energy localization in the low q fourier modes of fermi pasta ulam nonlinear lattices preventing equipartition among all modes at low energies in the first approach a low frequency fraction of the spectrum is initially excited leading to the formation of natural packets exhibiting exponential stability while in the second emphasis is placed on the existence of q breathers i e periodic continuations of the linear modes of the lattice which are exponentially localized in fourier space following ideas of the latter we introduce in this paper the concept of q tori representing exponentially localized solutions on low dimensional tori and use their stability properties to reconcile these two approaches and provide a more complete explanation of the fpu paradox

products of conjugacy classes in finite and algebraic simple groups abstract we prove the arad herzog conjecture for various families of finite simple groups if a and b are nontrivial conjugacy classes then a b is not a conjugacy class we also prove that if g is a finite simple group of lie type and a and b are nontrivial conjugacy classes either both semisimple or both unipotent then a b is not a conjugacy class we also prove a strong version of the arad herzog conjecture for simple algebraic groups and in particular show that almost always the product of two conjugacy classes in a simple algebraic group consists of infinitely many conjugacy classes as a consequence we obtain a complete classification of pairs of centralizers in a simple algebraic group which have dense product a special case of this has been used by prasad to prove a uniqueness result for tits systems in quasi reductive groups our final result is a generalization of the baer suzuki theorem for p elements with p 5

weyl submodules in restrictions of simple modules abstract let f be an algebraically closed field of characteristic p 0 suppose that sl n 1 f is naturally embedded into sl n f either in the top left corner or in the bottom right corner we prove that certain weyl modules over sl n 1 f can be embedded into the restriction l sl n 1 f where l is a simple sl n f module this allows us to construct new primitive vectors in l sl n 1 f from any primitive vectors in the corresponding weyl modules some examples are given to show that this result actually works

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

on 2 modular representations of the symmetric groups abstract let g gl n denote the general linear group of invertible n n matrices with entries in an algebraically closed field f of characteristic 2 we prove the existence of certain composition factors in the restriction to gl n k gl k of some polynomial g modules as a consequence we resolve the final case of the problem addressed by jantzen and seitz of when an irreducible modular representation of the symmetric group s n remains irreducible upon restriction to the young subgroup s n k s k

reconstruction from limited angle projections based on delta u spectrum analysis this paper proposes a sparse representation of an image using discrete u functions a u function is defined as the product of a kronecker delta function and a step function based on the sparse representation we have developed a novel and effective method for reconstructing an image from limited angle projections the method first estimates the parameters of the sparse representation from the incomplete projection data and then directly calculates the image to be reconstructed experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total variation tv regularized reconstruction method

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

on restrictions of modular spin representations of symmetric and alternating groups let f be an algebraically closed field of characteristic p and h be an almost simple group or a central extension of an almost simple group an important problem in representation theory is to classify the subgroups g of h and fh modules v such that the restriction v g is irreducible for example this problem is a natural part of the program of describing maximal subgroups in finite classical groups in this paper we investigate the case of the problem where h is the schur s double cover n or s n

on the limitations of the birkhoff gustavson normal form approach recently the birkhoff gustavson normal form bgnf approach has been used in both classical and semiclassical calculations the authors consider the limitations associated with this approach using as an illustration the anharmonic oscillator at the classical level they emphasise the need to properly take into account the divergence properties of the bgnf series by reviewing an earlier work they demonstrate that this divergence problem may in some cases be resolved however after considering several standard quantisation rules they find that it is not possible to obtain the correct quantisation of a system via the bgnf as a result they maintain that care should be used when working with the bgnf

globally convergent edge preserving regularized reconstruction an application to limited angle tomography we introduce a generalization of a deterministic relaxation algorithm for edge preserving regularization in linear inverse problems this algorithm transforms the original possibly nonconvex optimization problem into a sequence of quadratic optimization problems and has been shown to converge under certain conditions when the original cost functional being minimized is strictly convex we prove that our more general algorithm is globally convergent i e converges to a local minimum from any initialization under less restrictive conditions even when the original cost functional is nonconvex we apply this algorithm to tomographic reconstruction from limited angle data by formulating the problem as one of regularized least squares optimization the results demonstrate that the constraint of piecewise smoothness applied through the use of edge preserving regularization can provide excellent limited angle tomographic reconstructions two edge preserving regularizers one convex the other nonconvex are used in numerous simulations to demonstrate the effectiveness of the algorithm under various limited angle scenarios and to explore how factors such as the choice of error norm angular sampling rate and amount of noise affect the reconstruction quality and algorithm performance these simulation results show that for this application the nonconvex regularizer produces consistently superior results

on the jordan block structure of images of some unipotent elements in modular irreducible representations of the classical algebraic groups images of root elements in p restricted irreducible representations of the classical algebraic groups over a field of characteristic p 0 and images of regular unipotent elements of naturally embedded subgroups of type a2 in such representations of groups of type an with n 2 and p 2 are investigated let i 1nmi i be the highest weight of a representation under consideration if is locally small with respect to p in a certain sense the sizes of all jordan blocks without multiplicities in the images of root elements are found except the case of the groups of type bn and c2 and short roots where all such sizes congruent to mi 1 modulo 2 are determined with the ith simple root being short for p 2 and n 3 all odd dimensions of such blocks for groups of type an and regular unipotent elements of naturally embedded subgroups of type a2 are found here the class of locally small weights with respect to p depends upon the type of a group and upon elements considered for root elements in a group of type an the weight is locally small if mi mi 1 3 and regular unipotent elements of naturally embedded a2 subgroups the weight is locally small if mi mi 1 mi 2 mi 3 p 2 for some i with i n 2 for arbitrary p restricted representations the presence of blocks of certain sizes in the images of elements indicated above is established

representations of the alternating group which are irreducible over subgroups ii nsf dms 1161094 dms 0901241 dms 1201374 humboldt foundation simons foundation 204181 simons foundation fellowship 305247

nekhoroshev stability of elliptic equilibria of hamiltonian systems we prove a conjecture by n n nekhoroshev about the long time stability of elliptic equilibria of hamiltonian systems without any diophantine condition on the frequencies higher order terms of the hamiltonian are used to provide convexity the singularity of the action angle coordinates at the origin is overcome by working in cartesian coordinates

amorphous surface growth via a level set approach abstract we construct an equation for amorphous surface growth due to some deposition process within the level set approach and derive a unique viscosity solution to this equation from a source particles deposit on the initial hypersurface 0 in any direction and diffuse on the hypersurface for each time t we define thereby a hypersurface t

improved accuracy of the birkhoff gustavson normal form and its convergence properties the authors study the generalized henon heiles system by systematic exploration and analysis of the birkhoff gustavson normal form and the associated formal integral of motion up to and including the 14th order which is one order higher than published before at low energies the formal integral of motion is still an excellent approximation to the exact integral the convergence properties of the formal integral have been analysed in regular and irregular regions strictly convergent behaviour is found in some regions of chaotic motion no obvious example of divergent behaviour is found regions of strict convergence correspond either to regular motion or to weakly unstable chaotic motion with short time clustering characterized by a small value of the finite time analogue of the lyapunov exponent

invariants of specht modules abstract in 14 hemmer conjectures that the module of fixed points for the symmetric group m of a specht module for n with n m over a field of positive characteristic p has a specht series when viewed as a n m module we provide a counterexample for each prime p the examples have the same form for p 5 and we treat the cases p 3 and p 2 separately

on restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups i 1994 on restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups ii communications in algebra vol 22 no 15 pp 6175 6208

wavelet based reconstruction for limited angle x ray tomography the aim of x ray tomography is to reconstruct an unknown physical body from a collection of projection images when the projection images are only available from a limited angle of view the reconstruction problem is a severely ill posed inverse problem statistical inversion allows stable solution of the limited angle tomography problem by complementing the measurement data by a priori information in this work the unknown attenuation distribution inside the body is represented as a wavelet expansion and a besov space prior distribution together with positivity constraint is used the wavelet expansion is thresholded before reconstruction to reduce the dimension of the computational problem feasibility of the method is demonstrated by numerical examples using in vitro data from mammography and dental radiology

halo orbits around the collinear points of the restricted three body problem abstract we perform an analytical study of the bifurcation of the halo orbits around the collinear points l 1 l 2 l 3 for the circular spatial restricted three body problem following a standard procedure we reduce to the center manifold constructing a normal form adapted to the synchronous resonance introducing a detuning which measures the displacement from the resonance and expanding the energy in series of the detuning we are able to evaluate the energy level at which the bifurcation takes place for arbitrary values of the mass ratio in most cases the analytical results thus obtained are in very good agreement with the numerical expectations providing the bifurcation threshold with good accuracy care must be taken when dealing with l 3 for small values of the mass ratio between the primaries in that case the model of the system is a singular perturbation problem and the normal form method is not particularly suited to evaluate the bifurcation threshold

general runner removal and the mullineux map abstract we prove a new runner removal theorem for q decomposition numbers of the level 1 fock space of type a e 1 1 generalising earlier theorems of james mathas and the author by combining this with another theorem relating to the mullineux map we show that the problem of finding all q decomposition numbers indexed by partitions of a given weight is a finite computation

factorizations of simple algebraic groups we determine all factorizations of simple algebraic groups as the product of two maximal closed connected subgroups additional results are established which drop the maximality assumption and applications are given to the study of subgroups of classical groups transitive on subspaces of a given dimension

some remarks on branching rules and tensor products for algebraic groups let f be an algebraically closed field of characteristic p 0 in bk1 bk2 we have revealed and exploited various relations between the branching rules from gln f to its levi subgroups on one hand and decompositions of tensor products over gln f itself on the other for example if l is some irreducible rational gln f module and v is the natural gln f module there is a close relationship between the highest weight vectors relative to gln 1 f in the restriction l gln 1 f and the highest weight vectors relative to gln f in the tensor product l v in this paper we obtain more results in this direction some of which are valid for an arbitrary type to describe our main results we adopt standard lie theoretic notation let g be a connected reductive algebraic group over f as in j r denotes the root system of g with respect to a fixed maximal torus t r r denotes the set of positive roots determined by a choice of borel subgroup b containing t and 1 r is the corresponding base for r denote the highest long root of r by 0 and the longest element of the weyl group w ng t t by w0 we write x t for the character group hom t f y t for the cocharacter group hom f t and let be the natural pairing x t y t z for r denotes the corresponding coroot in y t and x t denotes the set x t i 0 i 1 of dominant weights all g modules are assumed to be rational for x t we have the g modules l and which are the irreducible the standard or weyl and the costandard gmodules with highest weight let dist g be the algebra of distributions of g as in j i 7 which is generated by dist t and the divided power root generators x y n for r n 1 write x i x n i yi y n i for i 1 if g is semisimple and simply connected which we may assume for the proofs dist g coincides with the hyperalgebra of g arising from the chevalley construction we note that any g module is a dist g module in a natural way see j i 7 11 ii 1 20 given a weight x t and a g module m m will denote the weight space of m if in addition x t is a dominant weight we define