PIRSA:20060036

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_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}}
          }
          

Pramod Achar Louisiana State University (LSU)

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.