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A colimit of traces of reflection groups

Author: Penghui Li
Journal: Proc. Amer. Math. Soc. 147 (2019), 4597-4604
MSC (2010): Primary 20F55; Secondary 18G99
Published electronically: June 10, 2019
MathSciNet review: 4011497
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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. As a corollary, we give an expression of the centralizer of a finite order element in a reflection group using homotopy theory.

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Additional Information

Penghui Li
Affiliation: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria

Received by editor(s): November 25, 2018
Received by editor(s) in revised form: January 27, 2019, and February 1, 2019
Published electronically: June 10, 2019
Additional Notes: The author is grateful for the support of Prof. Tamas Hausel and the Advanced grant “Arithmetic and physics of Higgs moduli spaces”, No. 320593 of the European Research Council.
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2019 American Mathematical Society