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

Raphaël Beuzart-Plessis (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: trace formula; relative Langlands program; harmonic analysis

Domaines: Mathématiques générales [math.GM]; Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Raphaël Beuzart-Plessis. On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad. Inventiones Mathematicae, 2018, 214 (1), pp.437-521. ⟨10.1007/s00222-018-0807-z⟩. ⟨hal-01941337⟩