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arXiv · 0809.1461

The spherical Hecke algebra for affine Kac-Moody groups I

Alexander Braverman·David Kazhdan
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Abstract

We define the spherical Hecke algebra for an (untwisted) affine Kac-Moody group over a local non-archimedian field. We prove a generalization of the Satake isomorphism for these algebras, relating it to integrable representations of the Langlands dual affine Kac-Moody group. In the next publication we shall use these results to define and study the notion of Hecke eigenfunction for the group $G_{\aff}$

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Alexander Braverman, David Kazhdan. 2010-09-15. The spherical Hecke algebra for affine Kac-Moody groups I. https://arxiv.org/abs/0809.1461

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