Abstract:
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 ⊗ k. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V ⊗ 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 ⊗ k-modules from weak V-modules. For an arbitrary permutation automorphism g of V ⊗ k the category of weak admissible g-twisted modules for V ⊗ 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 γg-twisted V ⊗ k-modules for γ a general automorphism of V acting diagonally on V ⊗ k and g a permutation automorphism of V ⊗ k.
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Received: 20 April 2000 / Accepted: 20 January 2002
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Barron, K., Dong, C. & Mason, G. Twisted Sectors for Tensor Product Vertex Operator Algebras Associated to Permutation Groups. Commun. Math. Phys. 227, 349–384 (2002). https://doi.org/10.1007/s002200200633
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DOI: https://doi.org/10.1007/s002200200633