F-symbols and R-symbols for the Drinfeld center of the Haagerup subfactor
Fabian M\"aurer, Ulrich Thiel, Gert Vercleyen
TL;DR
This paper presents an algorithm to compute explicit F-symbols, R-symbols, and pivotal coefficients for the Drinfeld center of the Haagerup subfactor, advancing understanding of fusion categories and their centers.
Contribution
It introduces a new algorithm for finding a minimal field gauge of a multiplicity-free fusion category and applies it to the Haagerup H3 category.
Findings
Explicit F-symbols, R-symbols, and pivotal coefficients for Z(H3)
A general algorithm for minimal field gauge of fusion categories
Implementation in TensorCategories.jl software
Abstract
We have recently devised and implemented an algorithm for computing the Drinfeld center of a fusion category in our software package \textsc{TensorCategories.jl}. By simplifying the field of definition of the F-symbols, R-symbols, and pivotal coefficients of the Haagerup H3 category, we were now able to compute explicit F-symbols, R-symbols, and pivotal coefficients for its Drinfeld center Z(H3). In this paper, we discuss how to access this data. We also present our new general algorithm for finding a gauge of a multiplicity-free fusion category in which the symbols belong to a minimal field.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry