We study a particular class of infinite-dimensional representations of osp(1|2n). These representations L n (p) are characterized by a positive integer p, and are the lowest component in the p-fold tensor product of the metaplectic representation of osp(1|2n). We construct a new polynomial basis for L n (p) arising from the embedding osp(1|2np) ⊃ osp(1|2n). The basis vectors of L n (p) are labelled by semi-standard Young tableaux, and are expressed as Clifford algebra valued polynomials with integer coefficients in np variables. Using combinatorial properties of these tableau vectors it is deduced that they form indeed a basis. The computation of matrix elements of a set of generators of osp(1|2n) on these basis vectors requires further combinatorics, such as the action of a Young subgroup on the horizontal strips of the tableau.

We study the effects of the branching [Formula: see text] on a particular class of simple infinite-dimensional [Formula: see text]-modules L( p) characterized by a positive integer p. In the first part (Sec. III), we use combinatorial methods, such as Young tableaux and Young subgroups, to construct a new basis for L( p) that respects this branching, and we express the basis elements explicitly in two distinct ways: first, as monomials of negative root vectors of [Formula: see text] acting on certain [Formula: see text]-highest weight vectors in L( p) and then as polynomials in the generators of [Formula: see text] acting on a [Formula: see text]-lowest weight vector in L( p). In the second part (Sec. IV), we use extremal projectors and the theory of Mickelsson–Zhelobenko algebras to give new explicit constructions of raising and lowering operators related to the branching [Formula: see text]. We use the raising operators to give new expressions for the elements of the Gel’fand–Zetlin basis for L( p) as monomials of operators from [Formula: see text] acting on a [Formula: see text]-lowest weight vector in L( p). We observe that the Gel’fand–Zetlin basis for L( p) is related to the basis constructed earlier in this paper by a triangular transition matrix. We end this paper (Sec. V) with a detailed example treating the case n = 3.