Mickelsson algebras and representations of Yangians (Q2880683)

This paper provides realizations (up to changing the action of the center) of irreducible finite dimensional modules over the Yangian \(Y(\mathfrak{gl}_n)\) and twisted Yangians \(Y(\mathfrak{sp}_n)\) and \(Y(\mathfrak{so}_n)\) as certain quotients of tensor products of symmetric and exterior powers of the vector space \(\mathbb{C}^n\) (in the last case of the twisted Yangians \(Y(\mathfrak{so}_n)\) the realization covers only modules on which the action of \(\mathfrak{so}_n\) integrates to the action of \(\mathrm{SO}_n\)). The construction and arguments are based on the theory of reductive dual pairs and on the representation theory of Mickelsson algebras.