Graded representation theory of symmetric groups and Hecke algebras
by Sasha Kleschev
Abstract: We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last years. The emphasis will be 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.
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