# The spherical Hecke algebra for affine Kac-Moody groups I - Mathematics > Representation Theory

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/