Conjectures on tilting modules and antispherical $p$-cells

Pramod N. Achar; William Hardesty; Simon Riche

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arXiv · 1812.09960

Conjectures on tilting modules and antispherical $p$-cells

Pramod N. Achar·William Hardesty·Simon Riche

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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.

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BibTeX RIS

Pramod N. Achar, William Hardesty, Simon Riche. 2018-12-24. Conjectures on tilting modules and antispherical $p$-cells. https://arxiv.org/abs/1812.09960

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