Alexander S. Kleshchev

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Let K be a field of characteristic p > 0, Era the symmetric group on n letters, Sn_1 < Lra the subgroup consisting of the permutations of the first« — 1 letters, and D k the irreducible ATn-module corresponding to a (/^-regular) partition X of n. In [9] we described the socle of the restriction D [T and obtained a number of other results which can be(More)
We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) cyclotomic Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki’s categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial(More)
We give a presentation for the finite W -algebra associated to a nilpotent matrix inside the general linear Lie algebra over C. In the special case that the nilpotent matrix consists of n Jordan blocks each of the same size l, the presentation is that of the Yangian of level l associated to the Lie algebra gln, as was first observed by Ragoucy and Sorba. In(More)
We introduce some new presentations for the Yangian associated to the Lie algebra gln. These presentations are parametrized by tuples of positive integers summing to n. At one extreme, for the tuple (n), the presentation is the usual RTT presentation of Yn. At the other extreme, for the tuple (1 ), the presentation is closely related to Drinfeld’s(More)
Introduction In 13] { 15] we have obtained results generalizing the classical Branching Theorem for symmetric groups to the case of modular representations. For example we have described the socle of the restriction, D # n?1 , of an arbitrary (modular) irreducible representation D of the symmetric group n to the natural subgroup n?1. In particular, it turns(More)
Kronecker or inner tensor products of representations of symmetric groups (and many other groups) have been studied for a long time. But even for the symmetric groups no reasonable formula for decomposing Kronecker products of two irreducible complex representations into irreducible components is available (cf. [7, 5]). An equivalent problem is to decompose(More)
1.1. Let k be an algebraically closed field, GLn(k) be the general linear group over k, and Σd be the symmetric group on d letters. For k = C, Frobenius and Schur discovered that the commuting actions of GLn(k) and Σd on V ⊗d can be used to relate the character theory of these two groups. For modular representations of these groups the relationship between(More)