Rough Notes Repository

2. Unitary solutions of the pentagon and hexagon equations

Date added: 18th January 2024

Description: Given a fusion ring, one might wish to determine all possible (braided) fusion categorifications along with the skeletal data (F and R-symbols) by solving the pentagon and hexagon equations. Approaching this task (even for small fusion rings) can be taxing. Below, you can find a small selection of handworked solutions for simple examples. Please note that I'm only considering unitary solutions over the complex field here.

Representations of the (generalised) Iwahori-Hecke algebra in unitary braided fusion categories

Date added: 6th November 2023

Description: Rough notes written as an extended response to a question ("Link invariants from Hecke relations of higher order") on MathOverflow.