An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type

Hsian-Yang Chen and Ching Hung Lam

Vol. 271 (2014), No. 1, 25–51

DOI: 10.2140/pjm.2014.271.25

Abstract

We study a coset vertex operator algebra (VOA) $\tilde{W}$ in the lattice VOA $V_{E_8^3}$. We show that the coset VOA $\tilde{W}$ is generated by nine Ising vectors such that any two Ising vectors generate a $3C$ subVOA $U_{3C}$, and the group generated by the corresponding Miyamoto involutions has shape $3^2:2$. This gives an explicit example for Majorana representations of the group $3^2:2$ of $3C$-pure type.

Keywords

vertex operator algebras, Ising vectors, Majorana representation

Mathematical Subject Classification 2010

Primary: 17B69

Secondary: 20B25

Milestones

Received: 13 May 2013

Revised: 27 January 2014

Accepted: 28 April 2014

Published: 10 September 2014