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SCHUR–WEYL DUALITY FOR HEISENBERG COSETS

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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Correspondence to S. KANADE.

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Supported by the NSERC discovery grant #RES0020460.

Supported by PIMS postdoctoral fellowship.

Supported by the Simons Foundation Grant #318755.

Supported by the Australian Research Council Discovery Projects DP1093910 and DP160101520.

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CREUTZIG, T., KANADE, S., LINSHAW, A.R. et al. SCHUR–WEYL DUALITY FOR HEISENBERG COSETS. Transformation Groups 24, 301–354 (2019). https://doi.org/10.1007/s00031-018-9497-2

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