A class of unitary irreducible representations of the Lie superalgebra osp(1|2n) 1

Abstract

Using the equivalence of the defining relations of the orthosymplectic Lie superalgebra osp(1|2n) to the defining triple relations of n pairs of parabose operators b± i we construct a class of unitary irreducible (infinite-dimensional) lowest weight representations V (p) of osp(1|2n). We introduce an orthogonal basis of V (p) in terms of Gelfand-Zetlin patterns, where the subalgebra u(n) of osp(1|2n) plays a crucial role and we present explicit actions of the osp(1|2n) generators.