Deligne-Lusztig duality and wonderful compactification

2017/01/25 by Bernstein, Joseph, Bezrukavnikov, Roman, Kazhdan, David · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1701.07329

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 the 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) 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 obtain a description of the Serre functor for representations of a p-adic group.

Cited by

• Poles of intertwining operators in terms of irreducible components of Lusztig's characteristic variety in type A

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• Deligne-Lusztig constructions for unipotent and p-adic groups
• Homological properties of representations of p-adic groups related to geometry of the group at infinity
• Decomposition of higher Deligne-Lusztig representations
• Sur la cohomologie des compactifications de variétés de Deligne-Lusztig
• Compactification des variétés de Deligne-Lusztig