Professor Alexander Stasinski alexander.stasinski@durham.ac.uk
Professor
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 SL2(Fq〚ϖ〛/(ϖ2))SL2(Fq〚ϖ〛/(ϖ2)), with odd q, the extended Deligne–Lusztig varieties do indeed afford all the irreducible representations.
Stasinski, A. (2011). Extended Deligne–Lusztig varieties for general and special linear groups. Advances in Mathematics, 226(3), 2825-2853. https://doi.org/10.1016/j.aim.2010.10.010
Journal Article Type | Article |
---|---|
Publication Date | Feb 15, 2011 |
Deposit Date | Mar 13, 2012 |
Publicly Available Date | May 7, 2014 |
Journal | Advances in Mathematics |
Print ISSN | 0001-8708 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 226 |
Issue | 3 |
Pages | 2825-2853 |
DOI | https://doi.org/10.1016/j.aim.2010.10.010 |
Keywords | Deligne–Lusztig varieties, Representations, Linear groups over finite rings. |
Public URL | https://durham-repository.worktribe.com/output/1502573 |
Accepted Journal Article
(258 Kb)
PDF
Copyright Statement
This is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 226, 3, 2011, 10.1016/j.aim.2010.10.010.
Rationality of twist representation zeta functions of compact p-adic analytic groups
(2024)
Journal Article
Representatives of similarity classes of matrices over PIDs corresponding to ideal classes
(2023)
Journal Article
A uniform proof of the finiteness of the class group of a global field
(2021)
Journal Article
Representations of SL over finite local rings of length two
(2020)
Journal Article
Representation growth of compact linear groups
(2019)
Journal Article
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
Apache License Version 2.0 (http://www.apache.org/licenses/)
Apache License Version 2.0 (http://www.apache.org/licenses/)
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2025
Advanced Search