Representations of the orthosymplectic Yangian

TL;DR

This paper classifies all finite-dimensional irreducible representations of the orthosymplectic Yangian associated with rak{osp}_{1|2}, providing explicit constructions and a tensor product framework.

Contribution

It offers a complete classification and explicit construction of irreducible representations of the orthosymplectic Yangian, a previously uncharacterized class.

Findings

Representations are parameterized by monic polynomials.

Explicit elementary modules are constructed.

Irreducible modules are generated via tensor products.

Abstract

We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra $\frak{osp}_{1|2}$. 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.