Finding bases of new infinite dimensional representations of $\mathfrak{osp}(1|2n)$ ( Dwight Williams, UT Arlington)

The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In this talk, we will define the orthosymplectic Lie superalgebras, realize $\mathfrak{osp}(1|2n)$ as differential operators on complex polynomials, and describe the space of polynomials in commuting and anti-commuting variables as a representation space for $\mathfrak{osp}(1|2n)$. Moreover, we will present operators—and perhaps generalized versions of these operators—which help give explicit bases for certain infinite dimensional $\mathfrak{osp}(1|2n)$-modules.