Conformal designs and minimal conformal weight spaces of vertex operator superalgebras

Tomonori Hashikawa

Vol. 284 (2016), No. 1, 121–145

DOI: 10.2140/pjm.2016.284.121

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 $2m$-design, then it also forms a conformal $\left(2m+1\right)$-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 ${\mathcal{S}}^5$.

Keywords

vertex operator superalgebra, conformal design, binary code

Mathematical Subject Classification 2010

Primary: 17B69

Milestones

Received: 15 November 2015

Accepted: 23 March 2016

Published: 10 July 2016