Deligne–Lusztig duality and wonderful compactification

Joseph Bernstein; Roman Bezrukavnikov; David Kazhdan

doi:10.1007/s00029-018-0391-5

Deligne–Lusztig duality and wonderful compactification

Joseph Bernstein
, Roman Bezrukavnikov^*
, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

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
Pages (from-to)	7-20
Number of pages	14
Journal	Selecta Mathematica, New Series
Volume	24
Issue number	1
DOIs	https://doi.org/10.1007/s00029-018-0391-5
State	Published - 1 Mar 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

Keywords

20G05
20G25
20J05
22E35

Access to Document

10.1007/s00029-018-0391-5

Cite this

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Deligne–Lusztig duality and wonderful compactification

Abstract

Bibliographical note

Keywords

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Correction to: Acknowledgments in six articles published in Selecta Mathematica (Selecta Mathematica, (2018), 24, 1, (473-497), 10.1007/s00029-017-0321-y)

Cite this

Deligne–Lusztig duality and wonderful compactification

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Related research output

Correction to: Acknowledgments in six articles published in Selecta Mathematica (Selecta Mathematica, (2018), 24, 1, (473-497), 10.1007/s00029-017-0321-y)

Cite this