Permutation orbifolds of the Heisenberg vertex algebra H(3)

We study the S3-orbifold of a rank three Heisenberg vertex algebra in terms of generators and relations. By using invariant theory, we prove that the orbifold algebra has a minimal strong generating set of vectors whose conformal weights are 1, 2, 3, 4, 5, 62 (two generators of degree 6). The structure of the cyclic Z3-orbifold is determined by similar methods. We also study characters of modules for the orbifold algebra.