Conjectures on p-cells, tilting modules, and nilpotent orbits
APA
Achar, P. (2020). Conjectures on p-cells, tilting modules, and nilpotent orbits. Perimeter Institute. https://pirsa.org/20060036
MLA
Achar, Pramod. Conjectures on p-cells, tilting modules, and nilpotent orbits. Perimeter Institute, Jun. 26, 2020, https://pirsa.org/20060036
BibTex
@misc{ pirsa_PIRSA:20060036, doi = {10.48660/20060036}, url = {https://pirsa.org/20060036}, author = {Achar, Pramod}, keywords = {Mathematical physics}, language = {en}, title = {Conjectures on p-cells, tilting modules, and nilpotent orbits}, publisher = {Perimeter Institute}, year = {2020}, month = {jun}, note = {PIRSA:20060036 see, \url{https://pirsa.org}} }
Louisiana State University (LSU)
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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 talk, I will review these results, and I will explain a (partly conjectural) analogous picture for reductive algebraic groups over fields of positive characteristic, inspired by a conjecture of Humphreys. This is joint work with W. Hardesty and S. Riche.