Representation theory of symmetric and spin symmetric groups and Lie theoryAlexander KleshchevUniversity of Oregon
March 21,

ABSTRACT


The goal of the talk is to explain few basic algebraic facts underlying representation theory of symmetric groups (the ideas are the same in characteristic 0 and p, for linear and projective representations, for Hecke algebras and affine Hecke algebras, etc. but we will concentrate on symmetric groups for simplicity). The key object is a maximal commutative subalgebra of the group algebra of the symmetric group which plays a role of a "maximal torus". Considering the corresponding "weight spaces" and "formal characters" leads to familiar combinatorial objects (partitions, Young tableaux, cores, etc.) However, these notions are nothing more than just one of several convenient combinatorial languages and the theory can be constructed from scratch using "Lie theoretic approach". The talk is bases on the work of Ariki, Grojnovski, OkounkovVershik, the speaker and the others. At least half of the talk requires nothing more than elemntary facts on representations of groups. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

