Moonshine for Rudvalis's sporadic group I

TL;DR

This paper constructs a new vertex operator superalgebra with enhanced conformal structure linked to the Rudvalis sporadic group, establishing an analogue of Monstrous Moonshine for this group and providing explicit series expressions.

Contribution

It introduces a refined vertex operator superalgebra associated with the Rudvalis group, extending Moonshine phenomena to a new sporadic group.

Findings

Construction of a self-dual vertex operator superalgebra with Rudvalis symmetry

Explicit formulas for McKay--Thompson series related to Rudvalis group

Establishment of Moonshine-like correspondence for Rudvalis group

Abstract

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.