ON A CLASS OF VERTEX OPERATOR ALGEBRAS HAVING A FAITHFUL Sn+1-ACTION

Abstract

By using the lattice VOA $V_{\sqrt{2}A_n}$, we construct a class of vertex operator algebras $\{M^{(n)}|\, n=2,3,4, \dots\}$ as coset subalgebras. We show that the VOA $M=M^{(n)}$ is generated by its weight $2$ subspace and the symmetric group $S_{n+1}$, which is isomorphic to the Weyl group $W(A_n)$ of the root system of type $A_n$, acts faithfully on $M$. Moreover, some irreducible modules of $M$ are constructed using the coset construction.