Duality for generalized Gan-Gross-Prasad relevant pairs for p-adic GL_n

2022/10/31 by Kei Yuen Chan, Chan, Kei Yuen
Mathematics · #20C08: 11F70 #22E50 #Advanced Algebra and Geometry #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2210.17249

openalex publication_date 2022/10/31 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28

Abstract

The main goal of this article is to formulate a notion, called a generalized GGP relevant pair, governing the quotient branching law for p-adic general linear groups. Such notion relies on a commutation relation between derivatives (from Jacquet functors) and integrals (from parabolic inductions), for which we provide both representation-theoretic and combinatorial perspectives. Our main result proves a duality on those relevant pairs, which is compatible with a dual restriction in branching law.

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