Conjectures on tilting modules and antispherical p-cells

Pramod N Achar (1) , William Hardesty (1) , Simon N. Riche (2)

1 LSU Mathematics - Department of Mathematics [Baton Rouge]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Domaines: Théorie des représentations [math.RT]

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