Rational and polynomial representations of Yangians (Q406367)

In the paper under review, the authors define natural classes of rational and polynomial modules of the Yangian \(Y(\mathfrak{gl}_n)\) of the general linear Lie algebra: the polynomial modules are subquotients of tensor products of vector modules, and the rational modules are subquotients of tensor products of vector and covector modules. It is shown that all simple polynomial and rational \(Y(\mathfrak{gl}_n)\)-modules arise as images of certain intertwining operators thus providing a classification and explicit realizations of all simple rational \(Y(\mathfrak{gl}_n)\)-modules.