Representation theory of symmetric groups and related Hecke algebras

Kleshchev, Alexander

doi:10.1090/S0273-0979-09-01277-4

Representation theory of symmetric groups and related Hecke algebras

Author: Alexander Kleshchev
Journal: Bull. Amer. Math. Soc. 47 (2010), 419-481
MSC (2000): Primary 20C30, 20C08, 17B37, 20C20, 17B67
DOI: https://doi.org/10.1090/S0273-0979-09-01277-4
Published electronically: October 27, 2009
MathSciNet review: 2651085
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Abstract: 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, etc.

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