Clebsch-Gordan and 6j-coefficients for rank two quantum groups

TL;DR

This paper computes and tabulates q-deformed Clebsch-Gordan and 6j-coefficients for rank two quantum groups, providing detailed methods and topological data relevant to related theories.

Contribution

It introduces explicit calculations and tabulations of these coefficients for rank two quantum groups, facilitating further research and applications.

Findings

Explicit tables of q-Clebsch-Gordan coefficients

Explicit tables of 6j-coefficients

Collected properties of fusion rules in conformal field theories

Abstract

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as well as some other topological data associated with theories corresponding to rank-two quantum groups. Finally, we collect some useful properties of the fusion rules of particular conformal field theories.