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.
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