Affine vertex operator superalgebra Losp(1|2)(l,0) at admissible level
Abstract
Let Losp(1|2)(l,0) be the simple affine vertex operator superalgebra with admissible level l. We prove that the category of weak Losp(1|2)(l,0)-modules on which the positive part of osp(1|2) acts locally nilpotent is semisimple. Then we prove that Q-graded vertex operator superalgebras (Losp(1|2)(l,0),ω) with new Virasoro elements ω are rational and the irreducible modules are exactly the admissible modules for osp(1|2), where 0<<1 is a rational number. Furthermore, we determine the Zhu's algebras A(Losp(1|2)(l,0)) and their bimodules A(L(l,j)) for (Losp(1|2)(l,0),ω), where j is the admissible weight. As an application, we calculate the fusion rules among the irreducible ordinary modules of (Losp(1|2)(l,0),ω).
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