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Every isometry s of a positive-definite even lattice Q can be lifted to anautomorphism of the lattice vertex algebra V_Q. An important problem in vertexalgebra theory and conformal field theory is to classify the representations ofthe s-invariant subalgebra V_Q^s of V_Q, known as an orbifold. In the case whens is an isometry of Q of order two, we have classified the irreducible modulesof the orbifold vertex algebra V_Q^s and identified them as submodules oftwisted or untwisted V_Q-modules in [Bavalov-Elsinger]. Here we calculate theirquantum dimensions and fusion products. The examples where Q is the orthogonaldirect sum of two copies of the A_2 root lattice and s is the 2-cyclepermutation as well as where Q is the A_n root latice and s is a Dynkin diagramautomorphism are presented in detail.

Quantum dimensions and fusion products for irreducible V_Q^s-modules, where s is an isometry of Q with s^2=1