Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras
章源慶教授成功大學數學系 15:30 – 17:00 鴻經館 M107
Abstract：
Let M be a tensor product of unitarizable irreducible highest weight modules over the Lie (super)algebra g, where g is gl(m|n), osp(2m|2n) or spo(2m|2n). We show that the singular eigenvectors of the quadratic Gaudin Hamiltonians for g on M can be obtained from the singular eigenvectors of the quadratic Gaudin Hamiltonians for the corresponding Lie algebras on some tensor products of finite-dimensional irreducible modules. Consequently, the simultaneous diagonalization of the quadratic Gaudin Hamiltonians for g on the singular space of M is established under a generic condition. This is joint work with Ngau Lam.