Abstract
We study the eigenvalues of the vertex set Hecke algebra of an affine building, and prove, by a direct approach, the Weyl group invariance 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.
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Mathematics Subject Classification (2010)
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Acknowledgements
We would like to acknowledge several useful suggestions of T. Steger during the preparation of this paper.
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Mantero, A.M., Zappa, A. (2013). Eigenvalues of the Vertex Set Hecke Algebra of an Affine Building. In: Picardello, M. (eds) Trends in Harmonic Analysis. Springer INdAM Series, vol 3. Springer, Milano. https://doi.org/10.1007/978-88-470-2853-1_12
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DOI: https://doi.org/10.1007/978-88-470-2853-1_12
Publisher Name: Springer, Milano
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