Diagonalisation of GL(N) invariant transfer matrices and quantum N-wave system (Lee model)

Abstract
The algebraic Bethe ansatz is constructed for the GL(N) invariant transfer matrices with arbitrary GL(N) spin. For this purpose the notion of vacuum subspace is introduced. It is shown that the GL(N) magnet can be interpreted as an integrable discrete approximation of vector or matrix nonlinear Schrodinger models or of the quantum N-wave system.