Representations of the super-Yangian of type $D(n,m)$

Abstract

We consider the classification problem for finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\mathfrak{osp}}_{2n|2m}$ with $n⩾2$. We give necessary conditions for an irreducible highest weight representation to be finite-dimensional. We conjecture that these conditions are also sufficient and prove the conjecture for a class of representations with linear highest weights. The arguments are based on a new type of odd reflections for the Yangian associated with ${\mathfrak{osp}}_{2|2}$. In the Appendix, we construct an isomorphism between the Yangians associated with the Lie superalgebras ${\mathfrak{osp}}_{2|2}$ and ${\mathfrak{gl}}_{1|2}$.

arXiv comment23 pages, extension of arXiv:2110.12784 to the series D(n,m)

References in corpus (11)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• The gl(M|N) Super Yangian and Its Finite Dimensional Representations
• On the R-matrix realization of Yangians and their representations
• R-matrix presentation for (super)-Yangians Y(g)
• Representations of Super Yangian
• Representations of the super Yangians of types $A$ and $C$
• Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$
• Representations of the Yangians associated with Lie superalgebras $\mathfrak{osp}(1|2n)$
• Representations of the orthosymplectic Yangian
• A Drinfeld-type presentation of the orthosymplectic Yangians
• Representations of the super-Yangian of type $B(n,m)$