The Satake Isomorphism for Special Maximal Parahoric Hecke Algebras
نویسندگان
چکیده
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. We also describe how our results relate to the treatment of Cartier [Car], where K is replaced by a special maximal compact open subgroup e K ⊂ G(F ) and where a Satake isomorphism is established for the Hecke algebra H e K .
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