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- W3106160500 abstract "We first exhibit two compatible Poisson structures on the cotangent bundle of the unitary group $$mathrm{U}(n)$$ in such a way that the invariant functions of the $${mathfrak {u}}(n)^*$$-valued momenta generate a bi-Hamiltonian hierarchy. One of the Poisson structures is the canonical one and the other one arises from embedding the Heisenberg double of the Poisson–Lie group $$mathrm{U}(n)$$ into $$T^*mathrm{U}(n)$$, and subsequently extending the embedded Poisson structure to the full cotangent bundle. We then apply Poisson reduction to the bi-Hamiltonian hierarchy on $$T^* mathrm{U}(n)$$ using the conjugation action of $$mathrm{U}(n)$$, for which the ring of invariant functions is closed under both Poisson brackets. We demonstrate that the reduced hierarchy belongs to the overlap of well-known trigonometric spin Sutherland and spin Ruijsenaars–Schneider-type integrable many-body models, which receive a bi-Hamiltonian interpretation via our treatment." @default.
- W3106160500 created "2020-11-23" @default.
- W3106160500 creator A5051880552 @default.
- W3106160500 date "2019-12-16" @default.
- W3106160500 modified "2023-09-26" @default.
- W3106160500 title "Reduction of a bi-Hamiltonian hierarchy on $$T^*mathrm{U}(n)$$ to spin Ruijsenaars–Sutherland models" @default.
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- W3106160500 doi "https://doi.org/10.1007/s11005-019-01252-1" @default.
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