# Bases for infinite dimensional simple $\mathfrak{osp}(1|2n)$-modules respecting the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$

@inproceedings{Bisbo2022BasesFI, title={Bases for infinite dimensional simple \$\mathfrak\{osp\}(1|2n)\$-modules respecting the branching \$\mathfrak\{osp\}(1|2n)\supset \mathfrak\{gl\}(n)\$}, author={Asmus K. Bisbo and Joris Van der Jeugt}, year={2022} }

We study the effects of the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$ on a particular class of simple infinite-dimensional $\mathfrak{osp}(1|2n)$-modules $L(p)$ characterized by a positive integer $p$. In the first part 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 $\mathfrak{gl…

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