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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

  • 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.


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