3 N ov 2 00 8 Moonshine for Rudvalis ’ s sporadic group I ∗

We introduce the notion of vertex operator superalgebra with enhanced conformal structure, which is a refinement of the notion of vertex operator superalgebra. We exhibit several examples, including a particular one which is self-dual, and whose full symmetry group is a direct product of a cyclic group of order seven with the sporadic simple group of Rudvalis. We thus obtain an analogue of Monstrous Moonshine for a sporadic group not involved in the Monster. Two variable analogues of the usual McKay–Thompson series are naturally associated to the action of the Rudvalis group on this object, and we provide explicit expressions for all the series arising.