Parity sheaves and the Hecke category

2018/01/03 by Williamson, Geordie · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1801.00896

Abstract

The Hecke category is emerging as a fundamental object in representation theory. We give a motivated introduction to this category in both its geometric (via parity sheaves) and diagrammatic (generators and relations) incarnations. We also discuss the p-canonical basis and Koszul duality for the Hecke category.

Cited by

• Tilting modules for reductive algebraic groups: characters and support varieties
• Semisimplifying categorical Heisenberg actions and periodic equivalences

Related

• The Hodge theory of the Hecke category
• Koszul duality for Coxeter groups
• Endoscopy for Modular Hecke Categories
• The p-Canonical Basis for Hecke Algebras
• Calculating the p-canonical basis of Hecke algebras