The algebraisation of higher Deligne–Lusztig representations

Chen, Zhe; Stasinski, Alexander

doi:10.1007/s00029-017-0349-z

The algebraisation of higher Deligne–Lusztig representations

Chen, Zhe; Stasinski, Alexander

Authors

Zhe Chen

Professor Alexander Stasinski alexander.stasinski@durham.ac.uk
Professor

Abstract

In this paper we study higher Deligne–Lusztig representations of reductive groups over finite quotients of discrete valuation rings. At even levels, we show that these geometrically constructed representations, defined by Lusztig, coincide with certain explicit induced representations defined by Gérardin, thus giving a solution to a problem raised by Lusztig. In particular, we determine the dimensions of these representations. As an immediate application we verify a conjecture of Letellier for GL2 and GL3.

Citation

Chen, Z., & Stasinski, A. (2017). The algebraisation of higher Deligne–Lusztig representations. Selecta Mathematica (New Series), 23(4), 2907-2926. https://doi.org/10.1007/s00029-017-0349-z

Journal Article Type	Article
Acceptance Date	Jun 27, 2017
Online Publication Date	Jul 15, 2017
Publication Date	Jul 15, 2017
Deposit Date	Jul 16, 2017
Publicly Available Date	Jul 17, 2017
Journal	Selecta Mathematica (New Series)
Print ISSN	1022-1824
Electronic ISSN	1420-9020
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	23
Issue	4
Pages	2907-2926
DOI	https://doi.org/10.1007/s00029-017-0349-z

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© The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.