Extended Deligne-Lusztig varieties for general and special linear groups

Details Extended Deligne-Lusztig varieties for general and special linear groups Extended Deligne-Lusztig varieties for general and special linear groups

2009-11-24

arxiv.org/abs/0911.4593v2

Mathematics

Representation Theory

28 pages. Shortened version, small corrections, Lemma 5.3 corrected. Discussion of open problems added

Scientific paper

We give a generalisation of Deligne-Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties to unramified maximal tori inside Borel subgroups. In this paper we associate a family of so-called extended Deligne-Lusztig varieties to all tamely ramified maximal tori of the group. Moreover, we analyse the structure of various generalised Deligne-Lusztig varieties, and show that the "unramified" varieties, including a certain natural generalisation, do not produce all the irreducible representations in general. On the other hand, we prove results which together with some computations of Lusztig show that for $\SL_{2}(\mathbb{F}_{q}[[\varpi]]/(\varpi^{2}))$, with odd $q$, the extended Deligne-Lusztig varieties do indeed afford all the irreducible representations.

Affiliated with

Also associated with

No associations

Rating

Extended Deligne-Lusztig varieties for general and special linear groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Extended Deligne-Lusztig varieties for general and special linear groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extended Deligne-Lusztig varieties for general and special linear groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-279774