Ribbon Categories of Weight Modules for Affine sl2 at Admissible Levels

Creutzig T, McRae R, Yang J (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Communications in Mathematical Physics Springer Verlag (Germany)

Book Volume: 407

Article Number: 123

Journal Issue: 6

DOI: 10.1007/s00220-026-05636-y

Abstract

We show that the braided tensor category of finitely-generated weight modules for the simple affine vertex operator algebra Lk(sl2) of sl2 at any admissible level k is rigid and hence a braided ribbon category. The proof uses a recent result of the first two authors with Shimizu and Yadav on embedding a braided Grothendieck-Verdier category C into the Drinfeld center of the category of modules for a suitable commutative algebra A in C, in situations where the braided tensor category of local A-modules is rigid. Here, the commutative algebra A is Adamović’s inverse quantum Hamiltonian reduction of Lk(sl2), which is the simple rational Virasoro vertex operator algebra at central charge 1-6(k+1)2k+2 tensored with a half-lattice conformal vertex algebra. As a corollary, we also show that the category of finitely-generated weight modules for the N=2 super Virasoro vertex operator superalgebra at central charge -6ℓ-3 is rigid for ℓ such that (ℓ+1)(k+2)=1.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie

Involved external institutions

Tsinghua University CN China (CN) Shanghai Jiao Tong University / 上海交通大学 CN China (CN)

How to cite

APA:

Creutzig, T., McRae, R., & Yang, J. (2026). Ribbon Categories of Weight Modules for Affine sl2 at Admissible Levels. Communications in Mathematical Physics, 407(6). https://doi.org/10.1007/s00220-026-05636-y

MLA:

Creutzig, Thomas, Robert McRae, and Jinwei Yang. "Ribbon Categories of Weight Modules for Affine sl2 at Admissible Levels." Communications in Mathematical Physics 407.6 (2026).

BibTeX: Download