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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- Penghui Li
- Affiliation: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
- Email: email@example.com
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 4597-4604
- MSC (2010): Primary 20F55; Secondary 18G99
- DOI: https://doi.org/10.1090/proc/14586
- MathSciNet review: 4011497