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

a new stability analysis of delayed cellular neural networks in this paper the global asymptotic stability of delayed cellular neural networks dcnns is investigated a novel criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented the criterion expressed by lmis is delay dependent the result is less conservative than those established in the earlier references a numerical example is given to show the effectiveness of proposed method

long time stability of kam tori for the generalized boussinesq equation abstract in this paper we prove that the kam tori for the generalized boussinesq equation with the external parameters which generates an infinite dimensional hamiltonian system are long time stable precisely we prove that the solutions with initial datum in the neighborhood of kam torus still stay close to the kam torus for t m with m 1 the proof is based on constructing a partial normal form of higher order and showing that the p tame property for the hamiltonian vector field persists after the changes of variables of the kam scheme and under normal form iterative procedure

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

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

representations of the alternating group which are irreducible over subgroups let f be an algebraically closed field of characteristic p geq 0 and a n be the alternating group on n letters the main goal of this paper is to describe the pairs g e where e is an irreducible fa n module and g 3 the case p 0 has been treated by j saxl the problem is important for the classification of maximal subgroups in finite classical groups 2000 mathematical subject classification 20c20 20c30 20b35 20b20

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

the non coprime k gv problem abstract let v be a finite faithful completely reducible fg module for a finite field f and a finite group g in various cases explicit linear bounds in v are given for the numbers of conjugacy classes k g v and k g of the semidirect product gv and of the group g respectively these results concern the so called non coprime k g v problem

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

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

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

delay dependent state estimation for delayed neural networks in this letter the delay dependent state estimation problem for neural networks with time varying delay is investigated a delay dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable the proposed method is based on the free weighting matrix approach and is applicable to the case that the derivative of a time varying delay takes any value an algorithm is presented to compute the state estimator finally a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones

lmi optimization approach on stability for delayed neural networks of neutral type in this paper the global asymptotic stability of delayed cellular neural networks of neutral type is investigated a novel delay dependent criterion for the stability using the lyapunov stability theory and linear matrix inequality lmi framework is presented since the condition is dependent on the size of time delay it is usually less conservative than delay independent ones two numerical examples are given to show the effectiveness of proposed method

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

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

global stability for cellular neural networks with time delay a sufficient condition related to the existence of a unique equilibrium point and its global asymptotic stability for cellular network networks with delay dcnns is derived it is shown that the condition relies on the feedback matrices and is independent of the delay parameter furthermore this condition is less restrictive than that given in the literature

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

on irreducible subgroups of simple algebraic groups let g be a simple algebraic group over an algebraically closed field k of characteristic p geqslant 0 let h be a proper closed subgroup of g and let v be a nontrivial irreducible kg module which is p restricted tensor indecomposable and rational assume that the restriction of v to h is irreducible in this paper we study the triples g h v of this form when g is a classical group and h is positive dimensional combined with earlier work of dynkin seitz testerman and others our main theorem reduces the problem of classifying the triples g h v to the case where g is an orthogonal group v is a spin module and h normalizes an orthogonal decomposition of the natural kg module

an analysis of global asymptotic stability of delayed cellular neural networks in this paper a new sufficient condition is given for the uniqueness and global asymptotic stability of the equilibrium point for delayed cellular neural networks dcnns this condition imposes constraints on the feedback and delayed feedback matrices of a dcnn independently of the delay parameter this result is also compared with the previous results derived in the literature