SCHUR–WEYL DUALITY FOR HEISENBERG COSETS

Creutzig T, Kanade S, Linshaw AR, Ridout D (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Transformation Groups Springer Verlag (Germany)

Book Volume: 24

Pages Range: 301-354

Journal Issue: 2

DOI: 10.1007/s00031-018-9497-2

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, 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.

Involved external institutions

University of Alberta

Canada (CA) University of Denver

United States (USA) (US)

How to cite

APA:

Creutzig, T., Kanade, S., Linshaw, A.R., & Ridout, D. (2019). SCHUR–WEYL DUALITY FOR HEISENBERG COSETS. Transformation Groups, 24(2), 301-354. https://doi.org/10.1007/s00031-018-9497-2

MLA:

Creutzig, T., et al. "SCHUR–WEYL DUALITY FOR HEISENBERG COSETS." Transformation Groups 24.2 (2019): 301-354.

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