Abstract

We use the Hamiltonian reduction method to construct the Ruisenaars dual systems togeneralized Toda chains associated with the classical Lie algebras of types B, C, D. The dualsystems tumn out to be the B, C, and D analogues of the rational Goldfish model, which is, as inthe type A case, the strong coupling limit of rational Ruisenaars systems. We explain how bothtypes of systems emerge in the reduction of the cotangent bundle of a Lie group and provide theformulae for dual Hamiltonians. We compute explicitly the higher Hamiltonians of Goldfish modelsusing the Cauchy-Binet theorem.

Joint work with Mikhail Vasilev, arXiv:2405.08620.