57 research outputs found
Decomposition matrices for low rank unitary groups
We study the decomposition matrices for the unipotent -blocks of finite
special unitary groups SU for unitary primes larger than . Up
to very few unknown entries, we give a complete solution for .
We also prove a general result for two-column partitions when divides
. This is achieved using projective modules coming from the -adic
cohomology of Deligne--Lusztig varieties
Deligne-Lusztig restriction of a Gelfand-Graev module
Using Deodhar's decomposition of a double Schubert cell, we study the regular
representations of finite groups of Lie type arising in the cohomology of
Deligne-Lusztig varieties associated to tori. We deduce that the
Deligne-Lusztig restriction of a Gelfand-Graev module is a shifted
Gelfand-Graev module.Comment: 18 page
- …