On Satake parameters for representations with parahoric fixed vectors

2014/02/16 by Thomas J. Haines, Haines, Thomas J.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1402.3812

openalex publication_date 2014/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article constructs the Satake parameter for any irreducible smooth J-spherical representation of a p-adic group, where J is any parahoric subgroup. This parametrizes such representations when J 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.

Citations

• Geometric structure and the local Langlands conjecture
• The Geometric Satake Correspondence for Ramified Groups

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