2018/08/02 by Paul Gustafson, Eric C. Rowell, Gustafson, Paul +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1808.00698
openalex publication_date 2018/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
N-Metaplectic categories, unitary modular categories with the same fusion rules as SO(N)2, are prototypical examples of weakly integral modular categories. As such, a conjecture of the second author would imply that images of the braid group representations associated with metaplectic categories are finite groups, i.e. have property F. While it was recently shown that SO(N)2 itself has property F, proving property F for the more general class of metaplectic modular categories is an open problem. We verify this conjecture for N-metaplectic modular categories when N is odd, exploiting their classification and enumeration to relate them to SO(N)2. In another direction, we prove that when N is divisible by 8 the N-metaplectic categories have 3 non-trivial bosons, and the boson condensation procedure applied to 2 of these bosons yields (N)/(4)-metaplectic categories. Otherwise stated: any 8k-metaplectic category is a ℤ2-gauging of a 2k-metaplectic category, so that the N even metaplectic categories lie towers of ℤ2-gaugings commencing with 2k- or 4k-metaplectic categories with k odd.