Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Olivier Dudas (Paris)

Title: Decomposition Numbers and Deligne-Lusztig Theory

Abstract: (Joint with Gunter Malle)

Two different problems arise when one tries to compute decomposition numbers for groups of Lie type:
(1) Determine cuspidal modules and their projective cover
(2) Compute the endomorphism algebra of the induced module
In this talk I will explain some recent progress on step (1). The construction of the missing projective modules is achieved using the cohomology of Deligne-Lusztig varieties, yielding new decomposition numbers for various unipotent blocks and various groups. The example of unitary groups is very instructive and I will use it to illustrate some (yet unexplained) patterns and conjectures on the decomposition numbers.