2011/05/25 by César Galindo, César Galíndo, Seung-Moon Hong +4
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CT #math.QA #msc:16W30 #msc:20F36
paper · pdf · doi:10.48550/arxiv.1105.5048
31 pages
arxiv created 2011/05/25 · arxiv updated 2011/05/26
We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang-Baxter operators in monoidal categories. The essential problem is to determine when a family of braid representations can be uniformly modelled upon a tensor power of a fixed vector space in such a way that the braid group generators act "locally". Although related to the notion of (quasi-)fiber functors for fusion categories, remarkably, such localizations can exist for representations associated with objects of non-integral dimension. We conjecture that such localizations exist precisely when the object in question has dimension the square-root of an integer and prove several key special cases of the conjecture.