Modular Representation Theory of Symmetric Groups

2014/05/13 by Kleshchev, Alexander
#20C30 #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1405.3326

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 FΣ_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.

Related

• Representation Theory of Symmetric Groups and Related Hecke Algebras
• Modular Representations, Old and New
• Modular representations of Hecke algebras
• Modular decomposition numbers of cyclotomic Hecke and diagrammatic Cherednik algebras: A path theoretic approach
• Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)