Deligne–Lusztig duality and wonderful compactification
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29_2018_391_ReferencePDF.pdf
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Author(s)
Bernstein, Joseph
Bezrukavnikov, Roman
Kazhdan, David
Date Issued
January 23, 2018
Publisher
Springer International Publishing
Version
Author's final manuscript
Abstract
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
$$G=GL(n)$$
G
=
G
L
(
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00029-018-0391-5
