Finite-gap difference opeators with elliptic coefficients and their spectral curves

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We review recent results on the finite-gap properties of difference operators with elliptic coefficients and give explicit characterization of spectral curves for difference analogues of the higher Lamé operators. This curve parametrizes double-Bloch solutions to the difference Lamé equation. The curve depends on a positive integer number \ell, related to its genus g by g=2\ell, and two continuous parameters: the lattice spacing ηand the modular parameter τ. Isospectral deformations of the difference Lamé operator under Volterra flows are also discussed.
Talk given at the workshop "Physical Combinatorics", (IIAS-RIMS, January 1999), 15 pages, LaTeX

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Quantum Algebra, Exactly Solvable and Integrable Systems, 39A70, 33E10

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http://salesiana.dossiersoluciones.com/handle/123456789/79260

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9910097
 http://arxiv.org/abs/math/9910097

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arXiv