Deligne–Lusztig duality and wonderful compactification

Joseph Bernstein, Roman Bezrukavnikov, David Kazhdan

Research output: Contribution to journalArticlepeer-review

Abstract

We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne–Lusztig (or Alvis–Curtis) duality for p-adic groups and homological duality. This provides a new way to introduce an involution on the set of irreducible representations of the group which has been defined by A. Zelevinsky for G= GL(n) and by A.-M. Aubert in general (less direct geometric approaches to this duality have been developed earlier by Schneider-Stuhler and by the second author). As a byproduct, we describe the Serre functor for representations of a p-adic group.

Original languageEnglish
Pages (from-to)7-20
Number of pages14
JournalSelecta Mathematica, New Series
Volume24
Issue number1
DOIs
StatePublished - 1 Mar 2018

Keywords

  • 20G05
  • 20G25
  • 20J05
  • 22E35

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