Ruijsenaars duality for B,C,D Toda chains: Ruijsenaars duality for B,C,D Toda chains: I. Sechin, M. Vasilev.

We use the Hamiltonian reduction method to construct the Ruijsenaars dual systems to generalized Toda chains associated with the classical Lie algebras of types B , C , D . The dual systems turn out to be the B, C and D analogues of the rational goldfish model, which is, as in the type A case, the strong coupling limit of rational Ruijsenaars systems. We explain how both types of systems emerge in the reduction of the cotangent bundle of a Lie group and provide the formulae for dual Hamiltonians. We compute explicitly the higher Hamiltonians of goldfish models using the Cauchy–Binet theorem. [ABSTRACT FROM AUTHOR]