Duality for generalized Gan-Gross-Prasad relevant pairs for $p$-adic ${\mathrm{GL}}_n$

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.

arXiv commentv4: 39 pages, title changed, more details added, several parts rewritten