Moonshine for Rudvalis's sporadic group I

Details Moonshine for Rudvalis's sporadic group I Moonshine for Rudvalis's sporadic group I

2006-09-15

arxiv.org/abs/math/0609449v2

Mathematics

Representation Theory

56 pages; minor revisions

Scientific paper

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.

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