Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart: "Irreducible representations of Khovanov-Lauda-Rouquier algebras"
Presenter
May 1, 2024
Keywords:
- key words Lie algebras
- Representation theory
- combinatorics
MSC:
- 05-XX - Combinatorics {For finite fields
- see 11Txx}
- 16-XX - Associative rings and algebras {For the commutative case
- see 13-XX}
- 17-XX - Nonassociative rings and algebras
- 20-XX - Group theory and generalizations
Abstract
The representation theory of KLR algebras categorifies quantum groups. In particular there is one simple (finite dimensional) KLR module for each node in the crystal graph B(\infty), and one can use crystal operators to construct them by taking a simple quotient of a particular induced module. In finite type there are several ways to do this, including the adapted string construction of Benkart-Kang-Oh-Park, as well as work of Kleshchev-Ram and McNamara. I'll discuss some of these results and related ideas.