A colimit of traces of reflection groups

TL;DR

This paper proves a Weyl group analogue of a conjecture about traces of Hecke categories, extending the understanding of the Betti Geometric Langlands Conjecture to reflection groups in Euclidean or hyperbolic space.

Contribution

It establishes a new result for traces of reflection groups, generalizing previous conjectures related to Hecke categories and the Betti Geometric Langlands framework.

Findings

Proved a Weyl group analogue of Li-Nadler's conjecture.

Extended the theorem to reflection groups in Euclidean or hyperbolic space.

Provided new insights into the structure of traces in geometric representation theory.

Abstract

Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti Geometric Langlands Conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space.