The Aubert-Zelevinsky involution for G2 and its associated Hecke algebras
Abstract
Motivated by the recent work of Aubert-Xu and the techniques in G. Muic's article, we provide examples of computations of the Aubert-Zelevinsky duality functor for the principal and mediate series of the exceptional group G2, and deduce corresponding results regarding the involution on the Hecke algebra side. These computations also allow us to confirm several instances of the Bernstein conjecture for G2. This article is developed from part of the author's PhD thesis.
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