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

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