Joseph Bernstein, Roman Bezrukavnikov, David Kazhdan
Published 2017-01-25Version 1
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 to homological duality. This provides a new way to introduce an involution on the set of irreducible representations of the group, which has been earlier defined by A. Zelevinsky for $G=GL(n)$ by A.-M. Aubert in general.
Modulo $\ell$-representations of $p$-adic groups $\mathrm{SL_n}(F)$
An analog of the Deligne-Lusztig duality for $(\mathfrak{g},K)$-modules
Hecke algebras and $p$-adic groups
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