SMS scnews item created by Catherine Meister at Tue 10 Mar 2026 1056
Type: Seminar
Distribution: World
Expiry: 24 Mar 2026
Calendar1: 13 Mar 2026 0900-1100
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
Auth: cmeister@10.136.67.203 (cmei0631) in SMS-SAML

Informal Friday Seminar

Modular reduction of complex representations of finite reductive groups

Morton-Ferguson

Calder Morton-Ferguson, Yale University


Informal Friday Seminar, 13th March 2026


9 am – 11 am, SMRI Seminar Room (A12 Macleay Room 301)


Abstract: Given a complex representation of a finite group, Brauer and Nesbitt defined in 1941 its reduction mod p, obtaining a representation over the algebraic closure of F_p. In 2021, Lusztig studied the characters obtained by reducing mod p an irreducible unipotent representation of a finite reductive group (itself over F_p). He gave a conjectural formula for this character as a linear combination of terms which had no explicit definition and were only known in some small-rank examples. In this talk, I will explain how to obtain an explicit formula for these terms and prove Lusztig’s conjecture, giving a formula for the reduction mod p of any unipotent representation of G(F_p). I will also explain a categorical interpretation of these results in terms of coherent sheaves on flag varieties. This is all joint work with Roman Bezrukavnikov, Michael Finkelberg, and David Kazhdan.

The Informal Friday Seminar is a space where members of our research group can explain interesting things to each other in a casual setting. The rules of the seminar are the following:

  1. Any question/additional explanation from the audience is allowed.
  2. Ego out the window.
  3. Examples, examples, examples.

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