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 Lam\'e 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 Y2=P(X2). We also compute the difference Galois group of the eigenvalue problem.
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