On the spectral curve of the difference Lamé operator

1998/12/30 by A. Zabrodin, Zabrodin, A. · 1 citation
Mathematics · Physics and Astronomy · #39A70 (Primary) 33E10 (Secondary) #Differential Equations and Boundary Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis #Quantum Algebra (math.QA) #hep-th #math.QA #msc:33E10 #msc:39A70 #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.math/9812161

22 pages, latex

arxiv created 1998/12/30 · openalex publication_date 1998/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give two "complementary" descriptions of the curve Γ parametrizing double-Bloch solutions to the difference analogue of the Lamé equation. The curve depends on a positive integer number ℓ and two continuous parameters: the "lattice spacing" η and the modular parameter τ. Apart from being a covering of the elliptic curve with the modular parameter τ, Γ is a hyperelliptic curve of genus 2ℓ. We also point out connections between the spectral curve and representations of the Sklyanin algebra.

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