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Article overview
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On Baxter Q-operators And Their Arithmetic Implications | | A. Gerasimov
; D. Lebedev
; S. Oblezin
; | | Date: |
18 Nov 2007 | | Abstract: | We consider Baxter Q-operators for various versions of quantum affine Toda
chain. The interpretation of eigenvalues of the Baxter operators as local
Archimedean L-functions proposed recently is generalized to affine Lie
algebras. We also propose a simple generalization of Baxter operators and local
L-functions compatible with this identification. This gives a connection of the
Baxter Q-operators for Toda chains with an Archimedean version of 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 also provide an Archimedean
analog of Casselman-Shalika-Shintani formula for Whittaker function in terms of
characters. Various conjectural arithmetical interpretations of the presented
results are discussed. | | Source: | arXiv, 0711.2812 | | Services: | Forum | Review | PDF | Favorites | |
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