Orbifolds of lattice vertex algebras under an isometry of order two

Every isometry σ of a positive-definite even lattice Q can be lifted to an automorphism of the lattice vertex algebra VQ. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the σ-invariant subalgebra VQσ of VQ, known as an orbifold. In the...

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Bibliographic Details
Published in:Journal of algebra 2015-11, Vol.441, p.57-83
Main Authors: Bakalov, Bojko, Elsinger, Jason
Format: Article
Language:English
Subjects:
Dynkin diagram automorphism
Intertwining operator
Lattice vertex algebra
Orbifold algebra
Twisted module
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Summary:Every isometry σ of a positive-definite even lattice Q can be lifted to an automorphism of the lattice vertex algebra VQ. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the σ-invariant subalgebra VQσ of VQ, 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 VQσ and identify them as submodules of twisted or untwisted VQ-modules. The examples where Q is a root lattice and σ is a Dynkin diagram automorphism are presented in detail.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2015.06.028