Alexander Kleshchev
Published 2014-05-13Version 1
We review some recent advances in modular representation theory of symmetric groups and related Hecke algebras. We discuss connections with Khovanov-Lauda-Rouquier algebras and gradings on the blocks of the group algebras $F\Sigma_n$, which these connections reveal; graded categorification and connections with quantum groups and crystal bases; modular branching rules and the Mullineaux map; graded cellular structure and graded Specht modules; cuspidal systems for affine KLR algebras and imaginary Schur-Weyl duality, which connects representation theory of these algebras to the usual Schur algebras of smaller rank.
Comments: This is an expository paper for ICM proceedings
Elementary divisors of Cartan matrices for symmetric groups
A new approach to the representation theory of the symmetric groups. IV. $ \Bbb Z_{2}$-graded groups and algebras
Stability and periodicity in the modular representation theory of symmetric groups
![QR code for arXiv:1405.3326 [math.RT]](http://oss.arxitics.com/images/favicon.svg)