Finite-gap difference opeators with elliptic coefficients and their spectral curves
量子代数
2007-05-23 v1 可精确求解与可积系统
solv-int
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 Lam\'e operators. This curve parametrizes double-Bloch solutions to the difference Lam\'e 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 \eta and the modular parameter \tau. Isospectral deformations of the difference Lam\'e operator under Volterra flows are also discussed.
关键词
引用
@article{arxiv.math/9910097,
title = {Finite-gap difference opeators with elliptic coefficients and their spectral curves},
author = {A. Zabrodin},
journal= {arXiv preprint arXiv:math/9910097},
year = {2007}
}
备注
Talk given at the workshop "Physical Combinatorics", (IIAS-RIMS, January 1999), 15 pages, LaTeX