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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Alexander Stasinski

Chen, Zhe & Stasinski, Alexander (2017). The algebraisation of higher Deligne–Lusztig representations. Selecta Mathematica 23(4): 2907-2926.

Author(s) from Durham

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.