Deligne–Lusztig duality and wonderful compactification

Joseph Bernstein ^[1] ; Roman Bezrukavnikov ^[2] ; David Kazhdan ^[3]
1. [1] Tel Aviv University
  
  Tel Aviv University
  
  Israel
2. [2] Massachusetts Institute of Technology
  
  Massachusetts Institute of Technology
  
  City of Cambridge, Estados Unidos
3. [3] Hebrew University of Jerusalem
  
  Hebrew University of Jerusalem
  
  Israel
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 1, 2018, págs. 7-20
Idioma: inglés
DOI: 10.1007/s00029-018-0391-5
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Resumen
- 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.