The Aubert-Zelevinsky involution for G₂ and its associated Hecke algebras

2025/05/23 by Qin, Chuan
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.17422

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.

Citations

• The Explicit Local Langlands Correspondence for G₂
• Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks
• Representations of rank two affine Hecke algebras

Related

• An involution for Hecke algebras
• Bernstein-Zelevinsky derivatives: a Hecke algebra approach
• Zelevinsky's involution at roots of unity
• A formal power series over a noncommutative Hecke ring and the rationality of the Hecke series for GSp₄
• The explicit Zelevinsky-Aubert duality