Algebraic integrability of the two-body Ruijsenaars operator

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.

17 pages, amslatex

References in corpus (2)

• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$