The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras
Representation Theory
2025-05-26 v1
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 , 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 . This article is developed from part of the author's PhD thesis.
Keywords
Cite
@article{arxiv.2505.17422,
title = {The Aubert-Zelevinsky involution for $G_2$ and its associated Hecke algebras},
author = {Chuan Qin},
journal= {arXiv preprint arXiv:2505.17422},
year = {2025}
}
Comments
34 pages, 1 figure