The University of Southampton
University of Southampton Institutional Repository

Extended Deligne-Lusztig varieties for general and special linear groups

Extended Deligne-Lusztig varieties for general and special linear groups
Extended Deligne-Lusztig varieties for general and special linear groups
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 such 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(F_q[[\varpi]]/(\varpi^2)), with odd q, the extended Deligne-Lusztig varieties do indeed afford all the irreducible representations
29pp
Stasinski, Alexander
94bd8be7-4b4f-4e22-875b-3628d8c2ca19
Stasinski, Alexander
94bd8be7-4b4f-4e22-875b-3628d8c2ca19

Stasinski, Alexander (2009) Extended Deligne-Lusztig varieties for general and special linear groups. Preprint, 29pp. (Submitted)

Record type: Article

Abstract

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 such 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(F_q[[\varpi]]/(\varpi^2)), with odd q, the extended Deligne-Lusztig varieties do indeed afford all the irreducible representations

This record has no associated files available for download.

More information

Submitted date: 24 November 2009

Identifiers

Local EPrints ID: 69678
URI: http://eprints.soton.ac.uk/id/eprint/69678
PURE UUID: 29b857f1-1109-4887-bcdf-e48f212d6e75

Catalogue record

Date deposited: 27 Nov 2009
Last modified: 10 Dec 2021 16:26

Export record

Contributors

Author: Alexander Stasinski

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×