Séminaire Algèbre Géométrie Algébrique Topologie Algébrique :

Le 22 mai 2025 à 10:00 - salle 430

Présentée par Dell'Arciprete Alice - University of York

Quiver presentations for KLR algebras and Hecke categories

The ultimate goal of representation theory is to obtain a complete understanding of the submodule structure of some algebraic objects. In this talk we will tackle this problem for KLR algebras through an exciting interplay with the diagrammatic Hecke categories of maximal parabolics of finite symmetric groups. We will start with an introduction of Kazhdan-Lusztig theory and the definition of these Hecke categories. Then, we will reveal how combinatorics (in the shape of Dyck tableaux) plays a huge role in understanding the structure of these algebras. Even further we go beyond just looking at sets of Dyck tableaux (which enumerate the Kazhdan-Lusztig polynomials) — we uncover the relationships for passing between them. This "meta-Kazhdan-Lusztig combinatorics" is, in fact, rich enough to fully determine the Ext-quiver and the relations presentation of these algebras.