On Baxter Q-operators And Their Arithmetic Implications
arXiv:0711.2812
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.
Typos are corrected,27 pages
References in corpus (5)
- Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
- Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism
- Eigenfunctions of $GL(N,\RR)$ Toda chain: The Mellin-Barnes representation
- Representation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model
- New Integral Representations of Whittaker Functions for Classical Lie Groups