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Abstract: We define the spherical Hecke algebra for an untwisted affine Kac-Moodygroup over a local non-archimedian field. We prove a generalization of theSatake isomorphism for these algebras, relating it to integrablerepresentations of the Langlands dual affine Kac-Moody group. In the nextpublication we shall use these results to define and study the notion of Heckeeigenfunction for the group $G {\aff}$



Author: Alexander Braverman, David Kazhdan

Source: https://arxiv.org/



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