Università degli Studi di Genova
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.
Affine buildings, Hecke algebras, Poisson kernels