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Quiver Hecke Algebras via Lyndon Bases

SPEAKER: David Hill

TITLE: Quiver Hecke Algebras via Lyndon Bases

ABSTRACT A remarkable family of algebras, which we call Quiver Hecke algebras (QHAs), were discovered by Khovanov and Lauda, and independent by Rouquier. These algebras categorify the positive half of the quantized enveloping algebra of an associated symmetrizable Kac-Moody algebra. In a recent paper, Kleshchev and Ram initiated a program to give an elementary framework for the representation theory of the QHAs of finite type using the combinatorics of Lyndon words. In this talk we report that this program has been completed. Time permitting, we will also discuss current work in progress including a generalization of the Zelevinsky involution for affine Hecke algebras to arbitrary QHAs, relations to D-modules, and the prospect of adapting the underlying combinatorics to quantum affine algebras.