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We prove an integral formula computing multiplicities of square-integrablerepresentations relative to Galois pairs over $p$-adic fields and we apply thisformula to verify two consequences of a conjecture of Dipendra Prasad. Oneconcerns the exact computation of the multiplicity of the Steinbergrepresentation and the other the invariance of multiplicities by transfer amonginner forms.

On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad