The algebraisation of higher Deligne–Lusztig representations

Zhe Chen ^[1] ; Alexander Stasinsk ^[1]
1. [1] Durham University
  
  Durham University
  
  Reino Unido
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 4, 2017, págs. 2907-2926
Idioma: inglés
DOI: 10.1007/s00029-017-0349-z
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Resumen
- 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.