Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/proc/14586
Published electronically: June 10, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [BH13] Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486
  • [Bou02] Nicolas Bourbaki, Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 2002. Translated from the 1968 French original by Andrew Pressley. MR 1890629
  • [BZN16] David Ben-Zvi and David Nadler, Betti geometric Langlands, Algebraic geometry: Salt Lake City 2015, Proc. Sympos. Pure Math., vol. 97, Amer. Math. Soc., Providence, RI, 2018, pp. 3–41. MR 3821166
  • [Li18] Penghui Li, Derived categories of character sheaves, preprint, arXiv:1803.04289, 2018.
  • [LN15] Penghui Li and David Nadler, Uniformization of semistable bundles on elliptic curves, preprint, arXiv:1510.08762, 2015.
  • [Lur12] Jacob Lurie, Higher algebra, 2012.
  • [Vin88] Ernest B. Vinberg, Geometry. ii, encyclopaedia of mathematical sciences, 29, 1988.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20F55, 18G99

Retrieve articles in all journals with MSC (2010): 20F55, 18G99


Additional Information

Penghui Li
Affiliation: Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
Email: pli@ist.ac.at

DOI: https://doi.org/10.1090/proc/14586
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