Orbifolds of lattice vertex algebras under an isometry of order two

2015/02/28 by Bojko Bakalov, Jason Elsinger · 1 citation
Mathematics · #math.QA #msc:17B69 #msc:81R10

paper · pdf · doi:10.1016/j.jalgebra.2015.06.028

published as Journal of Algebra 441 (2015), 57-83 · 27 pages; v2 typos fixed and a reference added

arxiv created 2015/07/17 · arxiv updated 2015/12/04

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 classify the irreducible modules of the orbifold vertex algebra V_Q^σ and identify them as submodules of twisted or untwisted V_Q-modules. The examples where Q is a root lattice and σ is a Dynkin diagram automorphism are presented in detail.

Cited by

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

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