QUASI-EXACTLY SOLVABLE DEFORMATIONS OF GAUDIN MODELS AND QUASI-GAUDINALGEBRAS

A new class of completely integrable models is constructed. These mode ls are deformations of the famous integrable and exactly solvable Gaud in models. In contrast with the latter, they are quasi-exactly solvabl e, i.e. admit the algebraic Bethe ansatz solution only for some limite d parts of the spectrum. An underlying algebra responsible for both th e phenomena of complete integrability and quasi-exact solvability is c onstructed. We call it ''quasi-Gaudin algebra'' and demonstrate that i t is a special non-Lie-algebraic deformation of the ordinary Gaudin al gebra.