English

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.

Keywords

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

R2 v1 2026-06-23T06:55:27.950Z