The B(G)-parametrization of the local Langlands correspondence

2022/11/25 by Alexander Bertoloni Meli, Meli, Alexander Bertoloni, Masao Oi +1
Mathematics · #11F70 #11S37 #22E50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.13864

openalex publication_date 2022/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article is on the parametrization of the local Langlands correspondence over local fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set (which is an extension of the set of pure inner twists) implies a parametrization indexed by the full Kottwitz set. On the Galois side, we consider irreducible algebraic representations of the full centralizer group of the L-parameter (i.e not a component group). When F is a p-adic field, we discuss a generalization of the endoscopic character identity.

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