Abstract:
The aim of this paper is to describe the eigenvalues of the vertex set Hecke algebra of an
affine building. We prove, by a direct approach, the invariance (with respect to the Weyl group) of
any eigenvalue associated to a character. Moreover we construct the Satake isomorphism of the Hecke
algebra and we prove, by this isomorphism, that every eigenvalue arises from a character.
Keywords:
Affine buildings, Hecke algebras, Poisson kernels
MSC:
20, 51
