We study the minimal models associated to osp(1 vertical bar 2), otherwise known as the fractional-level Wess- Zumino-Witten models of osp(1 vertical bar 2). Since these minimal models are extensions of the tensor product of certain Virasoro and 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 osp (1 vertical bar 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. (C) 2018 Published by Elsevier B.V.
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