Ruijsenaars duality for B, C, D Toda chains

Abstract: 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.

Joint work with Mikhail Vasilev, arXiv:2405.08620.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

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