Representation Theory of Symmetric Groups and Related Hecke Algebras

Details Representation Theory of Symmetric Groups and Related Hecke Algebras Representation Theory of Symmetric Groups and Related Hecke Algebras

2009-09-26

arxiv.org/abs/0909.4844v1

Mathematics

Representation Theory

Scientific paper

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, ...

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