On Realizing Modular Data

2019/10/15 by Parsa Bonderson, Eric C. Rowell, Bonderson, Parsa +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Computer science #Economics #FOS: Mathematics #Geometry #Grossman #Mathematics #Modular design #Modular invariance #Physics #Programming language #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #Symmetry (geometry) #Tensor (intrinsic definition) #Theoretical physics #math.QA

paper · pdf · doi:10.48550/arxiv.1910.07061

published in arXiv (Cornell University) 27(1), 65-79 (Cornell University)

arxiv created 2019/10/15 · openalex publication_date 2019/10/15 · arxiv updated 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use zesting and symmetry gauging of modular tensor categories to analyze some previously unrealized modular data obtained by Grossman and Izumi. In one case we find all realizations and in the other we determine the form of possible realizations; in both cases all realizations can be obtained from quantum groups at roots of unity.

Citations

• On the Structure of Modular Categories
• Fermionic Modular Categories and the 16-fold Way

Related

• Classification of modular data up to rank 12
• From Quantum Groups to Unitary Modular Tensor Categories
• Braided Zestings of Verlinde Modular Categories and Their Modular Data
• Quantum Groups at Roots of Unity and Modularity
• On inner product in modular tensor categories. I