Representations of the orthosymplectic Yangian

Abstract

We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra ${\mathfrak{osp}}_{1|2}$. The representations are parameterized by monic polynomials in one variable, they are classified in terms of highest weights. We give explicit constructions of a family of elementary modules of the Yangian and show that a wide class of irreducible representations can be produced by taking tensor products of the elementary modules.

28 pages, a few changes are made in the last section correcting a mistake in the initial version of the proof

References in corpus (3)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Yangians and Yang-Baxter R-operators for ortho-symplectic 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 $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$