Decomposition matrices for low rank unitary groups

Abstract

We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU${}_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\dots ,10$. We also prove a general result for two-column partitions when $\ell$ divides $q+1$. This is achieved using projective modules coming from the $\ell$-adic cohomology of Deligne--Lusztig varieties.

References in corpus (1)

• Minimal length elements of finite Coxeter groups