Twisted sectors for tensor product vertex operator algebras associated to permutation groups

Details Twisted sectors for tensor product vertex operator algebras associated to permutation groups Twisted sectors for tensor product vertex operator algebras associated to permutation groups

1998-03-24

arxiv.org/abs/math/9803118v2

Commun.Math.Phys. 227 (2002) 349-384

Mathematics

Quantum Algebra

amslatex 34 pages, both mathematics and typos are corrected

Scientific paper

10.1007/s002200200633

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V^{\otimes k} are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V^{\otimes k}-modules from weak V-modules. For an arbitrary permutation automorphism g of V^{\otimes k} the category of weak admissible g-twisted modules for V^{\otimes k$ is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of \gamma g-twisted V^{\otimes k}-modules for \gamma a general automorphism of V acting diagonally on V^{\otimes k} and a g a permutation automorphism of V^{\otimes k}.

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