Representations of the Yangians associated with Lie superalgebras $\mathfrak{osp}(1|2n)$

Abstract

We classify the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras ${\mathfrak{osp}}_{1|2n}$ in terms of the Drinfeld polynomials. The arguments rely on the description of the representations in the particular case $n=1$ obtained in our previous work.

10 pages, extension of arXiv:2108.10104 to arbitrary positive integers $n$

References in corpus (4)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Yangians and Yang-Baxter R-operators for ortho-symplectic superalgebras
• Yang-Baxter R-operators for osp superalgebras
• Isomorphism between two realizations of the Yangian Y(so_3)

Cited by in corpus (5)

• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Representations of the super-Yangian of type $B(n,m)$
• Representations of the super-Yangian of type $D(n,m)$
• Gaussian generators for the Yangian associated with the Lie superalgebra $\mathfrak{osp}(1|2m)$
• Bases for infinite dimensional simple $\mathfrak{osp}(1|2n)$-modules respecting the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$