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arXiv · 2210.17249

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

Kei Yuen Chan
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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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BibTeXRIS

Kei Yuen Chan. 2022-10-31. Duality for generalized Gan-Gross-Prasad relevant pairs for $p$-adic $\mathrm{GL}_n$. https://arxiv.org/abs/2210.17249

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