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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A colimit of traces of reflection groups
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by Penghui Li PDF
Proc. Amer. Math. Soc. 147 (2019), 4597-4604 Request permission

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
  • Email: pli@ist.ac.at
  • 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