Conformal designs and minimal conformal weight spaces of vertex operator superalgebras

Abstract

We give equivalent conditions for conformal designs of the minimal conformal weight spaces of SVOAs, and show that if the minimal conformal weight space of an SVOA forms a conformal 2 m-design, then it also forms a conformal .2m C 1/-design. Also, we derive trace formulae for the zero-modes of elements of the conformal weight 2 space on the minimal conformal weight space when the minimal conformal weight space forms a conformal 4-design. As an application of the trace formulae, we classify code SVOAs whose minimal conformal weight spaces form conformal 4-designs. Moreover, we show that the classified code SVOAs are of class S 5. MSC2010: 17B69.