On Baxter Q-operators And Their Arithmetic Implications

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We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of affine Lie algebras. We also introduce a simple generalization of Baxter operators and local L-functions compatible with this identification. This gives a connection of the Toda chain Baxter Q-operators with an Archimedean version of the Polya-Hilbert operator proposed by Berry-Kitting. We also elucidate the Dorey-Tateo spectral interpretation of eigenvalues of Q-operators. Using explicit expressions for eigenfunctions of affine/relativistic Toda chain we obtain an Archimedean analog of Casselman-Shalika-Shintani formula for Whittaker function in terms of characters.
Typos are corrected,27 pages

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Representation Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/157610

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0711.2812
 http://arxiv.org/abs/0711.2812

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arXiv