Ersatz parity sheaves and stratifications of KLR algebras

by Sasha Minets (MPIM Bonn)

Friday Apr 25, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/Room 1.008 (Mathezentrum)

Many important algebras, notably quiver Hecke algebras, can be realized as Ext-algebras of constructible sheaves on a space X. Since we like highest weight categories, we want to know when such algebras are quasi-hereditary (or polynomially quasi-hereditary, or properly stratified, etc). In characteristic zero, Kato proved a rather general result in this direction, under the assumption that X has finitely many orbits under the action of an algebraic group. This was extended to characteristic p by McNamara, replacing perverse sheaves techniques by parity sheaves of Juteau-Mautner-Williamson. Unfortunately, these results do not apply to KLR algebras beyond Dynkin type. I will explain how to extend the theory of parity sheaves to cover the first non-trivial case of Kronecker quiver. Based on arXiv:2504.xxxxx, joint with R. Maksimau.