Quantum-classical duality for Gaudin magnets with boundary

Nuclear Physics B - Proceedings Supplements. 2020. Vol. 952 . No. 114931. P. 1–20.

Васильев М., Zabrodin A., Zotov A.

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

Keywords: Gaudin models, integrable systems, Lie algebras, classical root system, Calogero-Moser model, quantum-classical duality, Gaudin Hamiltonians, quantum Gaudin models with boundary

Publication based on the results of: Developing methods of Representation Theory, Vertex Algebras and Geometry and Topology of Moduli spaces with applications to Combinatorics and Mathematical Physics (2020)