Deligne-Lusztig constructions for unipotent and p-adic groups

Abstract

In 1979 Lusztig proposed a conjectural construction of supercuspidal representations of reductive p-adic groups, which is similar to the well known construction of Deligne and Lusztig in the setting of finite reductive groups. We present a general method for explicitly calculating the representations arising from Lusztig's construction and illustrate it with several examples. The techniques we develop also provide background for the author's joint work with Weinstein on a purely local and explicit proof of the local Langlands correspondence.

50 pages, LaTeX

References in corpus (2)

• A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic
• Maximal varieties and the local Langlands correspondence for GL(n)

Cited by in corpus (9)

• Geometric realization of special cases of local Langlands and Jacquet-Langlands correspondences
• Maximal varieties and the local Langlands correspondence for GL(n)
• Affine Deligne-Lusztig varieties at infinite level
• On loop Deligne--Lusztig varieties of Coxeter-type for inner forms of ${\mathrm{GL}}_n$
• The cohomology of semi-infinite Deligne--Lusztig varieties
• Deligne--Lusztig constructions for division algebras and the local Langlands correspondence, II
• Orthogonality relations for deep level Deligne--Lusztig schemes of Coxeter type
• Ordinary $G{L}_2(F)$-representations in characteristic two via affine Deligne-Lusztig constructions
• The Drinfeld stratification for ${\mathrm{GL}}_n$