Conjectures on tilting modules and antispherical $p$-cells
Representation Theory
2019-04-16 v2
Abstract
For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii) Kazhdan-Lusztig cells in the affine Weyl group. In this paper, we propose a (partly conjectural) analogous picture for reductive algebraic groups over fields of positive characteristic, inspired by a conjecture of Humphreys.
Cite
@article{arxiv.1812.09960,
title = {Conjectures on tilting modules and antispherical $p$-cells},
author = {Pramod N. Achar and William Hardesty and Simon Riche},
journal= {arXiv preprint arXiv:1812.09960},
year = {2019}
}
Comments
16 pages. v2: minor corrections