Bi-Hamiltonian Structures of Spin Sutherland Models from Poisson Reduction

Explore a 52-minute lecture on bi-Hamiltonian structures of spin Sutherland models derived from Poisson reduction. Delve into the research findings presented by Lazlo Fehér at the Workshop on the Role of Integrable Systems, dedicated to John Harnad. Examine the natural quadratic Poisson bracket found in the holomorphic cotangent bundle T*GL(n,C) and its real forms, and how it relates to the canonical bracket. Discover how these structures lead to holomorphic and real trigonometric spin Sutherland models through reduction processes. Investigate the generalized Sutherland model coupled to two u(n)*-valued spins, resulting from the reduction of T*GL(n,C)_R. Learn about the interpretation of bi-Hamiltonian structures on the associative algebra gl(n,R) in the context of Toda models. Gain insights into how these reductions were previously studied using canonical Poisson structures, and understand the newly recognized bi-Hamiltonian aspect of these systems.