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

Abstract

We give a complete description of the finite-dimensional irreducible representations of the Yangians associated with the orthosymplectic Lie superalgebras mathfrak {osp}_{1|2n}. 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}. We show that a wide class of irreducible representations of this Yangian can be produced by taking tensor products of the elementary modules.