SCHUR–WEYL DUALITY FOR HEISENBERG COSETS

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...

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Published inTransformation groups Vol. 24; no. 2; pp. 301 - 354
Main Authors CREUTZIG, T., KANADE, S., LINSHAW, A. R., RIDOUT, D.
Format Journal Article
LanguageEnglish
Published New York Springer US 15.06.2019
Springer Nature B.V
Subjects
Algebra
Lie Groups
Mathematical analysis
Mathematics
Mathematics and Statistics
Modules
Tensors
Topological Groups
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Summary: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, C 2 -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 C 1 -cofiniteness of certain interesting classes of modules is established.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-018-9497-2