Representations of the Super Yangians of Types A and C

Abstract

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra mathfrak {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 mathfrak {gl}_{m|n}, as an appendix. This is a super-version of the well-known construction for the mathfrak {gl}_{n} Yangian and it relies on the Schur–Sergeev duality.