Deligne–Lusztig duality and wonderful compactification

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sword-2021-04-29T14:54:54.original.xml (130 B)
Original SWORD entry document
Date Issued
October 2018
Journal
Selecta Mathematica, New Series
Publisher
Springer Nature
Citation
2018. "Deligne–Lusztig duality and wonderful compactification." Selecta Mathematica, New Series, 24 (1).
Version
Author's final manuscript
Abstract
© 2018, Springer International Publishing AG, part of Springer Nature. 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.
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DOI of Published Version
10.1007/S00029-018-0391-5
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