Functions on the commuting stack via Langlands duality
Representation Theory
2024-04-16 v3 Algebraic Geometry
Abstract
We calculate the dg algebra of global functions on commuting stacks of complex reductive groups using tools from Betti Geometric Langlands. In particular, we prove that the ring of invariant functions on the commuting scheme is reduced. Our main technical results include: a semi-orthogonal decomposition of the cocenter of the affine Hecke category; and the calculation of endomorphisms of a Whittaker sheaf in a diagram organizing parabolic induction of character sheaves.
Cite
@article{arxiv.2301.02618,
title = {Functions on the commuting stack via Langlands duality},
author = {Penghui Li and David Nadler and Zhiwei Yun},
journal= {arXiv preprint arXiv:2301.02618},
year = {2024}
}
Comments
95 pages; to appear in Annals of Math