English

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

Representation Theory 2018-10-17 v2 Number Theory

Abstract

We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over pp-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.

Keywords

Cite

@article{arxiv.1707.06495,
  title  = {On distinguished square-integrable representations for Galois pairs and a conjecture of Prasad},
  author = {Raphaël Beuzart-Plessis},
  journal= {arXiv preprint arXiv:1707.06495},
  year   = {2018}
}

Comments

Includes corrections following the referee suggestions. Some proofs have been streamlined and a paragraph on `tempered pairs' (previously called strongly discrete pairs) has been added