%0 Journal Article
%T The Satake isomorphism for special maximal parahoric Hecke algebras
%A Thomas Haines
%A Sean Rostami
%J Mathematics
%D 2009
%I arXiv
%X 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 H 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, where K is replaced by a special maximal compact open subgroup K' of G(F) and where a Satake isomorphism is established for the Hecke algebra of K'-bi-invariant compactly supported functions on G(F).
%U http://arxiv.org/abs/0907.4506v2