A note on Integral Satake isomorphisms

2020/05/26 by Xinwen Zhu, Zhu, Xinwen · 4 citations
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic structures and combinatorial models #Chemistry #FOS: Mathematics #Hecke algebra #Isomorphism (crystallography) #Lattice (music) #Mathematical analysis #Mathematics #Physics #Pure mathematics #Representation Theory (math.RT) #Representation theory #math.RT

paper · pdf · doi:10.48550/arxiv.2005.13056

published in arXiv (Cornell University) (Cornell University) · A minor correction

openalex publication_date 2020/05/26 · arxiv created 2021/01/08 · arxiv updated 2021/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified p-adic group G and generalize the formulation to give a description of the Hecke algebra H_G(V) of weight V, where V is a lattice in an irreducible algebraic representation of G.

Citations

• A Satake isomorphism in characteristic p
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• On vector-valued twisted conjugate invariant functions on a group
• Banach-Hecke algebras and p-adic Galois Representations

Cited by

• Infinitesimal characters and Lafforgue's pseudocharacters
• Arithmetic and Geometric Langlands Program

Related

• A Satake homomorphism for the \bmod p derived Hecke algebra
• On the Satake isomorphism
• Iwahori-Hecke algebras for p-adic loop groups
• The Spherical Hecke algebra, partition functions, and motivic integration
• On Satake parameters for representations with parahoric fixed vectors