AbstractWe review our results on bi-Hamiltonian structures of trigonometric spin Sutherland models builton collective spin variables. Our basic observation was that the cotangent bundle T'*U(n) and itsholomorphic analogue T'*GL(n, C), as well as T"*GL(n, C)k, carry a natural quadratic Poissonbracket, which is compatible with the canonical linear one. The quadratic bracket arises by changeof va...
AbstractApplying the recently developed method-the off-diagonal Bethe ansatz method, we construct theexact solutions of the Heisenberg spin chain with various boundary conditions. The results allow usto calculate the boundary energy of the system in the thermodynamic limit. The method used herecan be generalized to study the thermodynamic properties and boundary energy of other high rankmodels ...
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