2018/12/24 by Pramod N. Achar, Achar, Pramod N., William Hardesty +3 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.1812.09960
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.