Year: 2024
Type: article
Abstract: For a complex reductive group, we construct a semi-orthogonal decomposition of the cocenter of the universal variant of its affine Hecke category. We use this to calculate the endomorphisms of a Whittaker object in the cocenter via a diagram organizing parabolic induction of character sheaves. Assuming a universal variant of Bezrukavnikov's spectral description of the affine Hecke category, we deduce a formula for the dg algebra of global functions on commuting stacks of complex reductive groups. In particular, the formula shows that the ring of invariant functions on the commuting scheme is reduced.
Source: Annals of Mathematics
Authors: Penghui Li, David Nadler, Zhiwei Yun
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402047218