Representation theory of lk (Osp(1|2)) from vertex tensor categories and jacobi forms

Creutzig T, Frohlich J, Kanade S (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Proceedings of the American Mathematical Society American Mathematical Society

Book Volume: 146

Pages Range: 4571-4589

Journal Issue: 11

DOI: 10.1090/proc/14066

Abstract

The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of vertex algebra extensions and modular forms. Let Lk (osp(1|2)) be the simple affine vertex operator superalgebra of osp(1|2) at an admissible level k. We use a Jacobi form decomposition to see that this is a vertex operator superalgebra extension of Lk (sl2) ⊗ Vir(p, (p + p′)/2) where k +3/2 = p/(2p′) and Vir(u, v) denotes the regular Virasoro vertex operator algebra of central charge c = 1− 6(u − v)2/(uv). Especially, for a positive integer k, we get a regular vertex operator superalgebra, and this case is studied further. The interplay of the theory of vertex algebra extensions and modular data of the vertex operator subalgebra allows us to classify all simple local (untwisted) and Ramond twisted Lk (osp(1|2))-modules and to obtain their super fusion rules. The latter are obtained in a second way from Verlinde’s formula for vertex operator superalgebras. Finally, using again the theory of vertex algebra extensions, we find all simple modules and their fusion rules of the parafermionic coset Ck = Com(VL, Lk (osp(1|2))), where VL is the lattice vertex operator algebra of the lattice L = √2kℤ.

Involved external institutions

University of Alberta CA Canada (CA)

How to cite

APA:

Creutzig, T., Frohlich, J., & Kanade, S. (2018). Representation theory of lk (Osp(1|2)) from vertex tensor categories and jacobi forms. Proceedings of the American Mathematical Society, 146(11), 4571-4589. https://doi.org/10.1090/proc/14066

MLA:

Creutzig, Thomas, Jesse Frohlich, and Shashank Kanade. "Representation theory of lk (Osp(1|2)) from vertex tensor categories and jacobi forms." Proceedings of the American Mathematical Society 146.11 (2018): 4571-4589.

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