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 -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