Representations of the Super Yangians of Types A and C

Abstract

AbstractWe classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra $\mathfrak {osp}_{2|2n}$ o s p 2 | 2 n . 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 $\mathfrak {gl}_{m|n}$ g l m | n , as an appendix. This is a super-version of the well-known construction for the $\mathfrak {gl}_{n}$ g l n Yangian and it relies on the Schur–Sergeev duality.