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.

arXiv comment28 pages, a few changes are made in the last section correcting a mistake in the initial version of the proof

References in corpus (13)

• Parabolic presentations of the Yangian Y(gl_n)
• 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)
• A new fusion procedure for the Brauer algebra and evaluation homomorphisms
• Bethe Ansatz equations and exact S matrices for the osp(M|2n) open super spin chain
• Equivalences between three presentations of orthogonal and symplectic Yangians
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double
• 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 $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$