Quantum dimensions and fusion products for irreducible VQσ-modules with σ2 = 1. Issue 7 (3rd July 2017) - Elsinger, Jason
ABSTRACT: Every isometry σ of a positive-definite even lattice Q can be lifted to an automorphism of the lattice vertex algebra V Q . An important problem in vertex algebra theory and conformal field theory is to classify the representations of the σ -invariant subalgebra V Q σ of V Q, known as an orbifold. In the case when σ is an isometry of Q of order two, we have classified the irreducible modules of the orbifold vertex algebra V Q σ and identified them as submodules of twisted or untwisted V Q -modules in [6 ]. Here we calculate their quantum dimensions and fusion products. The examples where Q is the orthogonal direct sum of two copies of the A 2 root lattice and σ is the 2-cycle permutation as well as where Q is the A n root lattice and σ is a Dynkin diagram automorphism are presented in detail.