Advertisement

Communications in Mathematical Physics

, Volume 227, Issue 2, pp 349–384 | Cite as

Twisted Sectors for Tensor Product Vertex Operator Algebras Associated to Permutation Groups

  • Katrina Barron
  • Chongying Dong
  • Geoffrey Mason

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 .

Keywords

Positive Integer General Setting Tensor Product Vertex Operator Operator Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Katrina Barron
    • 1
  • Chongying Dong
    • 1
  • Geoffrey Mason
    • 1
  1. 1.Department of Mathematics, University of California, Santa Cruz, CA 95064, USA.¶E-mail: dong@math.ucsc.edu; gem@math.ucsc.eduUS

Personalised recommendations