The spherical Hecke algebra for affine Kac-Moody groups I


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 this algebra, 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 $G_{\rm aff}$.


Alexander Braverman

Department of Mathematics
Brown University
Providence, RI 02912

David Kazhdan

Einstein Institute of Mathematics
The Hebrew University of Jerusalem,
Edmond J. Safra Campus, Givat Ram
Jerusalem 91904