An admissible level osp^ (1 | 2) -model: modular transformations and the Verlinde formula

The modular properties of the simple vertex operator superalgebra associated with the affine Kac–Moody superalgebra osp^ (1 | 2) at level -54 are investigated. After classifying the relaxed highest-weight modules over this vertex operator superalgebra, the characters and supercharacters of the simple weight modules are computed and their modular transforms are determined. This leads to a complete list of the Grothendieck fusion rules by way of a continuous superalgebraic analog of the Verlinde formula. All Grothendieck fusion coefficients are observed to be non-negative integers. These results indicate that the extension to general admissible levels will follow using the same methodology once the classification of relaxed highest-weight modules is completed.