PIRSA:20060036 Conference Mathematical physics

DOI10.48660/20060036

Conference/School: Geometric Representation Theory

Achar, P. (2020). Conjectures on p-cells, tilting modules, and nilpotent orbits. Perimeter Institute. https://pirsa.org/20060036

Achar, Pramod. Conjectures on p-cells, tilting modules, and nilpotent orbits. Perimeter Institute, Jun. 26, 2020, https://pirsa.org/20060036 

@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}}
}

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.

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