Quantum dimensions and fusion products for irreducible VQσ-modules with σ2 = 1. Issue 7 (3rd July 2017)

• Record Type: Journal Article
• Authors: Elsinger, Jason
• Is Part Of: Communications in algebra. Volume 45:Issue 7(2017)
• Page Start: 3091
• Page End: 3109
• Publication Date: 2017-07-03
• Subjects: Fusion product -- intertwining operator -- lattice vertex algebra -- orbifold -- quantum dimension -- twisted module; Primary 17B69 -- Secondary 81R10; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1235174
• Languages: English
• ISSNs: 0092-7872

Abstract

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.