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arXiv · 2505.17422

The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras

Chuan Qin
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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 $G_2$, 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 $G_2$. This article is developed from part of the author's PhD thesis.

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BibTeXRIS

Chuan Qin. 2025-05-23. The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras. https://arxiv.org/abs/2505.17422

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