The Satake isomorphism for special maximal parahoric Hecke algebras
By Thomas J. Haines, Sean Rostami. 2009
52 citations recorded by the source corpus.
Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. As an application we define a transfer homomorphism t : HK∗ (G∗) → HK(G) where G∗ is the quasi-split inner form of G. We also describe how our results relate to the treatment of Cartier [Car], where K is replaced by a special maximal compact open subgroup K ⊂ G(F ) and where a Satake isomorphism is established for the Hecke algebra H K .
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/89d7f31211d2aa6df2710128ec51eafc1de0ffb2
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Affine Grassmannians and Geometric Satake Equivalences (2013, background): “In [14], Haines and Rostami establish the Satake isomorphism for Hecke algebras of special parahoric subgroups.”