Representation Theory of Symmetric Groups and Related Hecke Algebras

Abstract

This 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, ...

References in corpus (7)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Blocks of cyclotomic Hecke algebras
• A new proof of the Mullineux conjecture
• Crystal structures arising from representations of $GL(m|n)$
• The modular branching rule for affine Hecke algebras of type A