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

Raphaël Beuzart-Plessis

doi:10.1007/s00222-018-0807-z

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

Raphaël Beuzart-Plessis

Université de Provence

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

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.

Original language	English
Pages (from-to)	437-521
Number of pages	85
Journal	Inventiones Mathematicae
Volume	214
Issue number	1
DOIs	https://doi.org/10.1007/s00222-018-0807-z
Publication status	Published - 1 Oct 2018
Externally published	Yes

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

Abstract

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