Fusion rules for the fixed point subalgebra of the vertex algebra associated with a non-degenerate and non-positive definite even lattice by an automorphism of order 2

Abstract

Let [Formula: see text] be the vertex algebra associated with a non-degenerate and non-positive definite even lattice [Formula: see text] and [Formula: see text] the fixed point subalgebra of [Formula: see text] under the action of the automorphism induced from the [Formula: see text]-isometry of [Formula: see text]. We determine the fusion rules for weak [Formula: see text]-modules. As an application of this result, we classify the irreducible weak modules for the fixed point subalgebra of [Formula: see text] under the action of the automorphism induced from an isometry of [Formula: see text] of order [Formula: see text]. We also show that every weak module for the same fixed point subalgebra is completely reducible.