On the unitarity and modularity of ribbon tensor categories associated with affine Lie algebras

2025/03/31 by Rudneva, Daria, Eddy Ardonne, Ardonne, Eddy
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2503.24348

openalex publication_date 2025/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the unitarity and modularity of ribbon tensor categories derived from simple affine Lie algebras, via their associated quantum groups. Based on numerical calculations, and assuming two conjectures, we provide the complete picture for which values of q these ribbon tensor categories are (pseudo-)unitary and for which values of q they are modular. We compare our results with the extensive rigorous results appearing in the literature, finding complete agreement. For the cases that do not appear in the literature, we complete the picture.

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