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On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad (1707.06495v2)

Published 20 Jul 2017 in math.RT and math.NT

Abstract: We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over $p$-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns the exact computation of the multiplicity of the Steinberg representation and the other the invariance of multiplicities by transfer among inner forms.

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