Ordinary modules for vertex algebras of osp1|2n

Creutzig T, Genra N, Linshaw A (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Journal für die reine und angewandte Mathematik

Book Volume: 2024

Pages Range: 1-31

Journal Issue: 817

DOI: 10.1515/crelle-2024-0060

Abstract

We show that the affine vertex superalgebra Vk(osp1|2n) at generic level k embeds in the equivariant W-algebra of sp2n times 4n free fermions. This has two corollaries: (1) it provides a new proof that, for generic k, the coset Com(Vk(sp2n), Vk(osp1|2n)) is isomorphic to (Wl(sp2n) for l = -(n + 1) + (k + n + 1)=(2k + 2n + 1), and (2) we obtain the decomposition of ordinary Vk (osp1|2n)-modules into Vk(sp2n) ⊗ Wl(sp2n)-modules. Next, if k is an admissible level and is a non-degenerate admissible level for sp2n, we show that the simple algebra Lk(osp1|2n) is an extension of the simple subalgebra Lk(sp2n) ⊗ Wl(sp2n). Using the theory of vertex superalgebra extensions, we prove that the category of ordinary Lk(osp1/2n)-modules is a semisimple, rigid vertex tensor supercategory with only finitely many inequivalent simple objects. It is equivalent to a certain subcategory of Wl(sp2n)-modules. A similar result also holds for the category of Ramond twisted modules. Due to a recent theorem of Robert McRae, we get as a corollary that categories of ordinary Lk(sp2n)-modules are rigid.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie

Involved external institutions

University of Tokyo JP Japan (JP) University of Denver US United States (USA) (US)

How to cite

APA:

Creutzig, T., Genra, N., & Linshaw, A. (2024). Ordinary modules for vertex algebras of osp1|2n. Journal für die reine und angewandte Mathematik, 2024(817), 1-31. https://doi.org/10.1515/crelle-2024-0060

MLA:

Creutzig, Thomas, Naoki Genra, and Andrew Linshaw. "Ordinary modules for vertex algebras of osp1|2n." Journal für die reine und angewandte Mathematik 2024.817 (2024): 1-31.

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