The algebraisation of higher Deligne–Lusztig representations

Chen, Zhe; Stasinski, Alexander

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
• Public URL: https://durham-repository.worktribe.com/output/1353217