Eric Rowell, "Braided weakly integral fusion categories"
An important algebraic invariant of fusion categories is the (global)
Frobenius-Perron dimension. Of particular interest is the dichotomy
integral and non-integral FP-dimension. There is good evidence to
that this (easily determined) dichotomy is related to some key
the braid group representations associated with braided fusion
I will discuss some conjectures in this vein.