Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties

Details Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties

2004-03-28

arxiv.org/abs/math/0403487v1

Mathematics

Representation Theory

10 pages

Scientific paper

In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local field, modulo a power of the maximal ideal. In this paper we define a generalisation of Lusztig's varieties, corresponding to an extension of the maximal unramified extension of the local field. We show in a particular case that all irreducible representations appear in the cohomology of some extended variety. We conclude with a discussion about reformulation of Lusztig's conjecture.

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