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On the spectral curve of the difference Lamé operator

A. Zabrodin
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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 $\ell$ 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 $2\ell$. We also point out connections between the spectral curve and representations of the Sklyanin algebra.

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A. Zabrodin. 1998-12-30. On the spectral curve of the difference Lamé operator. https://arxiv.org/abs/math/9812161

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