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

Abstract

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