Generalized and quasi-localizations of braid group representations Institutional Repository Document 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 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.

author list (cited authors)

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

complete list of authors

  • Galindo, C├ęsar||Hong, Seung-Moon||Rowell, Eric C

publication date

  • May 2011