Representations of the super Yangians of types \(A\) and \(C\)

A. I. Molev

Abstract

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra \({\frak osp}_{2|2n}\). The classification is given in terms of the highest weights and Drinfeld polynomials. We also include an \(R\)-matrix construction of the polynomial evaluation modules over the Yangian associated with the Lie superalgebra \({\frak gl}_{m|n}\), as an appendix. This is a super-version of the well-known construction for the \({\frak gl}_n\) Yangian and it relies on the Schur–Sergeev duality.