Speaker: Emily Norton (Kaiserslautern)
Title: New Decomposition Numbers of Finite Classical Groups
Abstract:
Gerber-Hiss-Jacon conjectured a combinatorial rule for the Harish-Chandra induction and restriction of modular unipotent representations of finite unitary groups. This conjecture was proved by Dudas-Varagnolo-Vasserot, who also showed that the combinatorial rule works for finite odd orthogonal and symplectic groups. However, their result has not been used so far in the study of decomposition numbers. I will explain a couple of arguments using the combinatorial rule to establish new decomposition numbers of these groups, including some "generic submatrices" of the decomposition matrix. This is joint work with Olivier Dudas.