Parity sheaves and the Hecke category

TL;DR

This paper introduces the Hecke category, exploring its geometric and diagrammatic forms, and discusses the p-canonical basis and Koszul duality, highlighting its significance in representation theory.

Contribution

It provides a motivated introduction to the Hecke category, connecting geometric and diagrammatic perspectives, and discusses advanced concepts like the p-canonical basis and Koszul duality.

Findings

Unified geometric and diagrammatic descriptions of the Hecke category

Discussion of the p-canonical basis in the context of the Hecke category

Insights into Koszul duality related to the Hecke category

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.