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arXiv · 2101.11484

Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case

L. Feher
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Abstract

We construct a bi-Hamiltonian structure for the holomorphic spin Sutherland hierarchy based on collective spin variables. The construction relies on Poisson reduction of a bi-Hamiltonian structure on the holomorphic cotangent bundle of GL(n,C), which itself arises from the canonical symplectic structure and the Poisson structure of the Heisenberg double of the standard GL(n,C) Poisson--Lie group. The previously obtained bi-Hamiltonian structures of the hyperbolic and trigonometric real forms are recovered on real slices of the holomorphic spin Sutherland model.

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BibTeXRIS

L. Feher. 2021-01-27. Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case. https://doi.org/10.1007/s00023-021-01084-7

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