English

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 JJ-spherical representation of a pp-adic group, where JJ is any parahoric subgroup. This parametrizes such representations when JJ 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.

Keywords

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

R2 v1 2026-06-22T03:09:13.655Z