English

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 FΣnF\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.

Keywords

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

R2 v1 2026-06-22T04:13:28.984Z