On Baxter Q-operators And Their Arithmetic Implications

A. Gerasimov; D. Lebedev; S. Oblezin

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arXiv · 0711.2812

On Baxter Q-operators And Their Arithmetic Implications

A. Gerasimov·D. Lebedev·S. Oblezin

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Abstract

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.

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BibTeX RIS

A. Gerasimov, D. Lebedev, S. Oblezin. 2008-03-30. On Baxter Q-operators And Their Arithmetic Implications. https://arxiv.org/abs/0711.2812

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