Modular Representation Theory of Symmetric Groups
Representation Theory
2014-05-15 v1 Group Theory
Quantum Algebra
Abstract
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 , 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.
Cite
@article{arxiv.1405.3326,
title = {Modular Representation Theory of Symmetric Groups},
author = {Alexander Kleshchev},
journal= {arXiv preprint arXiv:1405.3326},
year = {2014}
}
Comments
This is an expository paper for ICM proceedings