This paper studies the eigenvalues of the vertex set Hecke algebra of an affine building. We prove, by a direct approach, the invariance (with respect to theWeyl group) of any eigenvalue associated to a character. Moreover we construct the Satake isomorphismof the Hecke algebra and we prove, by this isomorphism, that every eigenvalue arises from a character.
Eigenvalues of the vertex set Hecke algebra of an affine building
MANTERO, ANNA MARIA;ZAPPA, ANNA
2013-01-01
Abstract
This paper studies the eigenvalues of the vertex set Hecke algebra of an affine building. We prove, by a direct approach, the invariance (with respect to theWeyl group) of any eigenvalue associated to a character. Moreover we construct the Satake isomorphismof the Hecke algebra and we prove, by this isomorphism, that every eigenvalue arises from a character.
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