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

23 pages, minor changes, references added, extension of arXiv:2109.02361

References in corpus (3)

• Representations of twisted Yangians associated with skew Young diagrams
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• Odd reflections in the Yangian associated with $\mathfrak{g}l(m|n)$

Cited by in corpus (8)

• A note on odd reflections of super Yangian and Bethe ansatz
• Lax Operator and superspin chains from 4D CS gauge theory
• Orthosymplectic superoscillator Lax matrices
• 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 $B(n,m)$
• Orthosymplectic Yangians
• Representations of the super-Yangian of type $D(n,m)$
• Gaussian generators for the Yangian associated with the Lie superalgebra $\mathfrak{osp}(1|2m)$