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Conjectures on tilting modules and antispherical p-cells

Abstract

For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik) 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.
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Dates and versions

hal-01968446 , version 1 (02-01-2019)

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Pramod N Achar, William Hardesty, Simon N. Riche. Conjectures on tilting modules and antispherical p-cells. 2019. ⟨hal-01968446⟩
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