Exponential modules of $\mathfrak{osp}(1|2)$

Abstract

We study properties of two families, $E_{+}(g)$ and $E_{-}(g)$, of non-weight modules over the orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ that are parameterized by a nonconstant polynomial $g(x)\in \mathbb{C}[x]$. These families appear naturally from the two oscillator homomorphisms and the exponential modules over the first Weyl algebra $\mathcal{D}(1)$. We prove simplicity and isomorphism theorems for $E_{+}(g)$ and $E_{-}(g)$.