Bershadsky-Polyakov vertex algebras at positive integer levels and duality

2020/11/19 by Dražen Adamović, Adamovic, Drazen, Ana Kontrec +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2011.10021

openalex publication_date 2020/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the simple Bershadsky-Polyakov algebra \mathcal W_k = W_k(sl₃,f_θ) at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from arXiv:1910.13781. Next, we study the case k=1. We discover that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple afine vertex superalgebra L_k' (osp(1 \vert 2)) for k'=-5/4. Using the free-field realization of L_k' (osp(1 \vert 2)) from arXiv:1711.11342, we get a free-field realization of \mathcal W_k and their highest weight modules. In a sequel, we plan to study fusion rules for \mathcal W_k.

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