Decomposition numbers for unipotent blocks with small $sl_2$-weight in finite classical groups

Abstract: There are many familiar module categories admitting a categorical action of a Lie algebra. The combinatorial shadow of such an action often yields answers to module-theoretic questions, for instance via crystals. In proving a conjecture of Gerber, Hiss, and Jacon, it was shown by Dudas, Varagnolo, and Vasserot that the category of unipotent representations of a finite classical group has such a categorical action. In this talk I will explain how we can use the categorical action to deduce closed formulas for certain families of decomposition numbers of these groups. This is joint work in progress with Olivier Dudas.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.