Representations of the Lie Superalgebra osp(1|2n) with Polynomial Bases

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