Gaudin-type models, non-skew-symmetric classical r -matrices and nested Bethe ansatz

T. Skrypnyk
2015 Nuclear Physics B  
We consider quantum integrable systems associated with the Lie algebra gl(n) and Cartan-invariant non-dynamical non-skew-symmetric classical r-matrices. We describe the sub-class of Cartan-invariant non-skew-symmetric r-matrices for which exists the standard procedure of the nested Bethe ansatz associated with the chain of embeddings gl(n) ⊃ gl(n − 1) ⊃ gl(n − 2) ⊃ · · · ⊃ gl(1). We diagonalize the corresponding quantum integrable systems by its means. We illustrate the obtained results by the
more » ... ned results by the examples of the generalized Gaudin systems with and without external magnetic field associated with three classes of non-dynamical non-skew-symmetric classical r-matrices.
doi:10.1016/j.nuclphysb.2014.12.004 fatcat:ie3rdl4njfff5pjxflg353txjm