Permutation Orbifolds of the Heisenberg Vertex Algebra $\mathcal{H}(3)$

Abstract

We study the $S_3$-orbifold of a rank three Heisenberg vertex algebras in terms of generators and relations. By using invariant theory we prove that the orbifold algebra has a minimal strongly generating set of vectors whose conformal weights are $1,2,3,4,5,6^2$ (two generators of degree $6$). The structure of the cyclic ${\mathbb{Z}}_3$-oribifold is determined by similar methods. We also study modular properties of characters of modules for these vertex algebras.

21 pages, to appear in J.Math.Physics

References in corpus (1)

• Representations of the vertex operator algebra V_{L_{2}}^{A_{4}}

Cited by in corpus (2)

• On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebra
• Vertex Algebras and Commutative Algebras