The Geometric Satake Correspondence for Ramified Groups

2011/07/28 by Xinwen Zhu, Zhu, Xinwen · 2 citations
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) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1107.5762

35 pages, with an appendix joint with Timo Richarz. New materials added in Section 6. arXiv admin note: text overlap with arXiv:1012.5979 by other authors

openalex publication_date 2011/07/28 · arxiv created 2012/12/27 · arxiv updated 2013/01/01 · 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
• On the coherence conjecture of Pappas and Rapoport

Cited by

• On Satake parameters for representations with parahoric fixed vectors
• Arithmetic and Geometric Langlands Program

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• Affine Grassmannians and Geometric Satake Equivalences
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