Alexander Kleshchev
Representation Theory of Symmetric Groups and Related Hecke Algebras.
Tue, 09/29/2009 - 15:21 — SomNambulAuthors: Alexander Kleshchev
Subjects: Representation Theory
AbstractThis is an expository article. We survey some fundamental trends in
representation theory of symmetric groups and related objects which became
apparent in the last fifteen years. The emphasis is on connections with Lie
theory via categorification. We present results on branching rules and crystal
graphs, decomposition numbers and canonical bases, graded representation
theory, connections with cyclotomic and affine Hecke algebras,
Khovanov-Lauda-Rouquier algebras, category ${\mathcal O}$, $W$-algebras, ...Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Alexander Kleshchev, Arun Ram
Subjects: Representation Theory
AbstractWe construct irreducible representations of affine Khovanov-Lauda-Rouquier
algebras of arbitrary finite type. The irreducible representations arise as
simple heads of appropriate induced modules, and thus our construction is
similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type
A. The highest weights of irreducible modules are given by the so-called good
words, and the highest weights of the 'cuspidal modules' are given by the good
Lyndon words. In a sense, this has been predicted by Leclerc.Representations of Khovanov-Lauda-Rouquier Algebras and Combinatorics of Lyndon Words.
Fri, 09/11/2009 - 19:12 — SomNambulAuthors: Alexander Kleshchev, Arun Ram
Subjects: Representation Theory
AbstractWe construct irreducible representations of affine Khovanov-Lauda-Rouquier
algebras of arbitrary finite type. The irreducible representations arise as
simple heads of appropriate induced modules, and thus our construction is
similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type
A. The highest weights of irreducible modules are given by the so-called good
words, and the highest weights of the 'cuspidal modules' are given by the good
Lyndon words. In a sense, this has been predicted by Leclerc.
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