Abstract
AbstractWe 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 $$\mathrm{GL}(n,\mathbb {C})$$
GL
(
n
,
C
)
, which itself arises from the canonical symplectic structure and the Poisson structure of the Heisenberg double of the standard $$\mathrm{GL}(n,\mathbb {C})$$
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.
Funder
european regional development fund and the budget of hungary
NKFIH
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
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