The spherical Hecke algebra for affine Kac-Moody groups I

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 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 $G_{\rm aff}$.

Authors

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
Israel