Standard modules and intertwining operators for reductive p-adic groups

2025/12/21 by Maarten Solleveld, Solleveld, Maarten
Mathematics · #20G25 #22E30 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2512.18685

openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

Consider a reductive group G over a non-archimedean local field. The Galois group Gal(C/Q) acts naturally on the category of smooth complex G-representations. We prove that this action stabilizes the class of standard modules. This generalizes and relies on an analogous result about essentially square-integrable representations. Other important objects in the proof of our main result are intertwining operators between parabolically induced G-representations, and the associated Harish-Chandra μ-functions. We determine an explicit formula for the μ-function of any irreducible representation of any Levi subgroup of G.

Citations

• Rationality properties of complex representations of reductive p-adic groups
• The universal Harish-Chandra j-function
• On parameters of Hecke algebras for p-adic groups
• Intertwining operators for representations of covering groups of reductive p-adic groups
• On the central value of Rankin L-functions for self-dual algebraic representations of linear groups over totally real fields
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• On the spectral decomposition of affine Hecke algebras

Cited by

• Rationality properties of complex representations of reductive p-adic groups

Related

• Intertwining operators for representations of covering groups of reductive p-adic groups
• Rationality properties of complex representations of reductive p-adic groups
• Some results on the admissible representations of non-connected reductive p-adic groups
• Modulo p representations of reductive p-adic groups: functorial properties
• On Representations of Reductive p--adic Groups over \mathbb Q--algebras