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

英文摘要：

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.