On Satake parameters for representations with parahoric fixed vectors
Representation Theory
2014-11-21 v3
Abstract
This article constructs the Satake parameter for any irreducible smooth -spherical representation of a -adic group, where is any parahoric subgroup. This parametrizes such representations when is a special maximal parahoric subgroup. The main novelty is for groups which are not quasi-split, and the construction should play a role in formulating a geometric Satake isomorphism for such groups over local function fields.
Cite
@article{arxiv.1402.3812,
title = {On Satake parameters for representations with parahoric fixed vectors},
author = {Thomas J. Haines},
journal= {arXiv preprint arXiv:1402.3812},
year = {2014}
}
Comments
Theorem 1.3 and Lemma 4.9 added. Minor correction made in proof of Proposition 4.1. Lemma 10.2 added. Accepted version. 26 pages