2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79260We 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, LaTeXQuantum AlgebraExactly Solvable and Integrable Systems39A70, 33E10text