Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case
| Autor: | László Fehér |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Reduction (recursion theory) Holomorphic function Structure (category theory) FOS: Physical sciences 01 natural sciences Poisson manifold 0103 physical sciences 0101 mathematics Mathematics::Symplectic Geometry Mathematical Physics Spin-½ Mathematical physics Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems Group (mathematics) 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) Nonlinear Sciences::Exactly Solvable and Integrable Systems High Energy Physics - Theory (hep-th) Cotangent bundle Condensed Matter::Strongly Correlated Electrons 010307 mathematical physics Exactly Solvable and Integrable Systems (nlin.SI) Symplectic geometry |
| DOI: | 10.48550/arxiv.2101.11484 |
| Popis: | 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. Comment: Expanded to 20 pages, contains a simplified formula of the second reduced Poisson bracket, more detailed derivations, and added references |
| Databáze: | OpenAIRE |
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