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It is known that the defining relations of the orthosymplectic Liesuperalgebra osp(1|2n) are equivalent to the defining (triple) relations of npairs of paraboson operators $b^\pm_i$. In particular, with the usual starconditions, this implies that the ``parabosons of order p'' correspond to aunitary irreducible (infinite-dimensional) lowest weight representation V(p) ofosp(1|2n). Apart from the simple cases p=1 or n=1, these representations hadnever been constructed due to computational difficulties, despite theirimportance. In the present paper we give an explicit and elegant constructionof these representations V(p), and we present explicit actions or matrixelements of the osp(1|2n) generators. The orthogonal basis vectors of V(p) arewritten in terms of Gelfand-Zetlin patterns, where the subalgebra u(n) ofosp(1|2n) plays a crucial role. Our results also lead to character formulas forthese infinite-dimensional osp(1|2n) representations. Furthermore, byconsidering the branching $ osp(1|2n) \supset sp(2n) \supset u(n)$, we findexplicit infinite-dimensional unitary irreducible lowest weight representationsof sp(2n) and their characters.

The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)