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SCHUR–WEYL DUALITY FOR HEISENBERG COSETS

  • T. CREUTZIG
  • S. KANADE
  • A. R. LINSHAW
  • D. RIDOUT
Article

Abstract

Let V be a simple vertex operator algebra containing a rank n Heisenberg vertex algebra H and let C = Com(H;V) be the coset of H in V. Assuming that the module categories of interest are vertex tensor categories in the sense of Huang, Lepowsky and Zhang, a Schur-Weyl type duality for both simple and indecomposable but reducible modules is proven. Families of vertex algebra extensions of C are found and every simple C-module is shown to be contained in at least one V-module. A corollary of this is that if V is rational, C2-cofinite and CFT-type, and Com(C;V) is a rational lattice vertex operator algebra, then C is likewise rational. These results are illustrated with many examples and the C1-cofiniteness of certain interesting classes of modules is established.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • T. CREUTZIG
    • 1
  • S. KANADE
    • 1
    • 2
  • A. R. LINSHAW
    • 2
  • D. RIDOUT
    • 3
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsUniversity of DenverDenverUSA
  3. 3.School of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

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