Multiplicity formula for induced representations: Bessel and Fourier-Jacobi models over Archimedean local fields

2023/08/05 by Cheng Chen, Chen, Cheng · 1 citation
Mathematics · #Advanced Algebra and Geometry #Spectral Theory in Mathematical Physics #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2308.02912

Abstract

This article proves a formula relating the multiplicity of an induced representation and that of the inducing datum for the Bessel and the Fourier-Jacobi models over Archimedean local fields by generalizing the approach of C. Moeglin and J.-L. Waldspurger in [MW12], which was successful for Bessel models of special orthogonal groups over non-Archimedean local fields. As an application, we give a uniform proof of the local Gan-Gross-Prasad conjecture for all classical groups over Archimedean local fields for generic local L-parameters based on the tempered basic cases.

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• Non-tempered Gan-Gross-Prasad conjecture for Archimedean general linear groups

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