Seminar in Representation Theory
Ersatz parity sheaves and stratifications of KLR algebras
2025/11/04 (Tue.) 15:00~16:00
- Date : 2025/11/04 (Tue.) 15:00~16:00
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Alexandre Minets (Max Planck Institute for Mathematics)
- Abstract :
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:2504.17430, joint with R. Maksimau.
