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
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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.