Kazhdan-Lusztig theory

Tuesday, 24-Sep-2024 

Abstract

Kazhdan-Lusztig theory seeks to reduce deep questions about the structure of objects in representation-theoretic, geometric, algebraic and diagrammatic categories to concrete questions about bases of Hecke algebras. In this talk, I will give an introduction to some of the categories that arise in this field  (Category O, perverse sheaves on flag varieties, Soergel modules, Elias-Williamson categories) and explain the equivalences between them. I’ll conclude by noting how much more difficult these problems become when the categories are k-linear over a field of characteristic p.