The Geometric Satake Correspondence for Ramified Groups

2011/07/28 by Xinwen Zhu, Zhu, Xinwen · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1107.5762

openalex publication_date 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the Rapoport-Zink-Pappas local models.

Citations

• Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian
• Kloosterman sheaves for reductive groups

Cited by

• On Satake parameters for representations with parahoric fixed vectors

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