Quantum dimensions and fusion products for irreducible V_Q^s-modules, where s is an isometry of Q with s²=1

2016/08/24 by Jason Elsinger, Elsinger, Jason
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.1608.06885

This paper is a continuation of the study of irreducible representations of orbifold vertex operator algebras corresponding to order 2 automorphisms done in [Bakalov-Elsinger]. arXiv admin note: text overlap with arXiv:1502.04756

arxiv created 2016/08/24 · arxiv updated 2016/08/25

Abstract

Every isometry s 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 s-invariant subalgebra V_Q^s of V_Q, known as an orbifold. In the case when s is an isometry of Q of order two, we have classified the irreducible modules of the orbifold vertex algebra V_Q^s and identified them as submodules of twisted or untwisted V_Q-modules in [Bavalov-Elsinger]. Here we calculate their quantum dimensions and fusion products. The examples where Q is the orthogonal direct sum of two copies of the A₂ root lattice and s is the 2-cycle permutation as well as where Q is the A_n root latice and s is a Dynkin diagram automorphism are presented in detail.

Citations

• Orbifolds of lattice vertex algebras under an isometry of order two

Related

• Orbifolds of lattice vertex algebras under an isometry of order two
• On Orbifold Theory
• The 3-permutation orbifold of a lattice vertex operator algebra
• Super orbifold theory
• Cyclic permutations of lattice vertex operator algebras