We study the minimal models associated to $\mathfrak{ osp}(1 \vert 2)$, otherwise known as the fractional-level Wess-Zumino-Witten models of $\mathfrak{ osp}(1 \vert 2)$. Since these minimal models are extensions of the tensor product of certain Virasoro and $\mathfrak{ sl}_2$ minimal models, we can induce the known structures of the representations of the latter models to get a rather complete understanding of the minimal models of $\mathfrak{ osp}(1 \vert 2)$. In particular, we classify the irreducible relaxed highest-weight modules, determine their characters and compute their Grothendieck fusion rules. We also discuss conjectures for their (genuine) fusion products and the projective covers of the irreducibles.
Categories: hep-th math-ph math.MP math.QA