Generalized and Quasi-Localizations of Braid Group Representations Academic Article uri icon

abstract

  • We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang-Baxter (YB) 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. © 2012 The Author(s). Published by Oxford University Press. All rights reserved.

author list (cited authors)

  • Galindo, C., Hong, S., & Rowell, E. C.

citation count

  • 15

publication date

  • January 2013