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 language | English |
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Pages (from-to) | 7-20 |
Number of pages | 14 |
Journal | Selecta Mathematica, New Series |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - 1 Mar 2018 |
Bibliographical note
Publisher Copyright:© 2018, Springer International Publishing AG, part of Springer Nature.
Keywords
- 20G05
- 20G25
- 20J05
- 22E35