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The algebraisation of higher Deligne–Lusztig representations.

Chen, Zhe and Stasinski, Alexander (2017) 'The algebraisation of higher Deligne–Lusztig representations.', Selecta mathematica., 23 (4). 2907-2926.


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.

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Publisher statement:© The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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.
Date accepted:27 June 2017
Date deposited:17 July 2017
Date of first online publication:15 July 2017
Date first made open access:No date available

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