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Algebraic integrability of the two-body Ruijsenaars operator

Giovanni Felder·Alexander Varchenko
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Abstract

We study the algebra of difference operators that commute with the two-body Ruijsenaars operator, a $q$-deformation of the Lamé differential operator, for generic values of the deformation parameter. The algebra is commutative. It is the algebra of polynomial functions on an affine hyperelliptic curve $Y^2=P(X^2)$. We also compute the difference Galois group of the eigenvalue problem.

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BibTeXRIS

Giovanni Felder, Alexander Varchenko. 1996-10-18. Algebraic integrability of the two-body Ruijsenaars operator. https://arxiv.org/abs/q-alg/9610024

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