Hecke categories, idempotents, and commuting stacks

TL;DR

This paper establishes a precise connection between a topological category derived from the affine Hecke category and a geometric category involving the equivariant derived category of the commuting stack, enhancing previous proposals.

Contribution

It formulates a detailed link between the idempotent completion of the trace of the affine Hecke category and the equivariant derived category of the semi-nilpotent commuting stack.

Findings

Identifies a correspondence between topological and geometric categories.

Provides an improved formulation of the connection compared to previous work.

Enhances understanding of the structure of Hecke categories and commuting stacks.

Abstract

We formulate a connection between a topological and a geometric category. The former is the idempotent completion of the (horizontal) trace of the affine Hecke category, while the latter is the equivariant derived category of the (semi-nilpotent) commuting stack. This provides a more precise and improved version of our proposal in [13].