We make a new multivariate generalization of the type A monomial space of asingle variable. It is different from the previously introduced type A space ofseveral variables which is an sl(M+1) module, and we thus call it type A'. Weconstruct the most general quasi-solvable operator of (at most) second-orderwhich preserves the type A' space. Investigating directly the condition underwhich the type A' operators can be transformed to Schroedinger operators, weobtain the complete list of the type A' quasi-solvable quantum many-bodysystems. In particular, we find new quasi-solvable models of deformedCalogero-Sutherland type which are different from the Inozemtsev systems. Wealso examine a new multivariate generalization of the type C monomial spacebased on the type A' scheme.
展开▼
