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Inventiones mathematicae

, Volume 214, Issue 1, pp 437–521 | Cite as

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

  • Raphaël Beuzart-PlessisEmail author
Article

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.

Notes

Acknowledgements

I am grateful to Jean-Loup Waldspurger for a very careful proofreading of a first version of this paper. I also thank the referee for correcting many inaccuracies and for the numerous comments to make the text more readable. The author has benefited from a Grant of Agence Nationale de la Recherche with reference ANR-13-BS01-0012 FERPLAY.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.I2M-CNRS(UMR 7373)Université d’Aix-MarseilleMarseille Cédex 9France

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