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 ${\mathfrak{o}\mathfrak{s}\mathfrak{p}}_{2|2n}$. 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 ${\mathfrak{g}\mathfrak{l}}_{m|n}$, as an appendix. This is a super-version of the well-known construction for the ${\mathfrak{g}\mathfrak{l}}_n$ Yangian and it relies on the Schur–Sergeev duality.