Some mathematica notebooks
Clebsch-Gordan and 6j coefficients for rank two quantum groups
These notebooks contain the q-CG coefficients for su(2)_k and rank two quantum groups based on affine Lie algebra's (at the lowest, non-trivial level, as well as a simple example of a theory with a fusion multiplicity). The q-6j symbols (for the rank two quantum groups) are calculated from the q-CG coefficients, and the pentagon equations are checked explicitly in this case.
- q-CG coefficients for su(2)_k: q-CG-su2k.nb.
- q-6j symbols for su(2)_k: q-6j-su2k.nb.
- q-CG coefficients for rank two quantum groups: q-CG-rank2.nb.
- q-6j symbols for rank two quantum groups: q-6j-rank2.nb.
The explicit formula for the su(2)_k q-CG coefficients can be found in
V.A. Groza, I.I. Kachurik, A.U. Klimyk, J. Math. Phys. 31, 2769 (1990).
The su(2)_k q-6j symbols are based on the
formula of Kirillov and Reshetikhin:
A.N. Kirillov, N.Y. Reshetikhin, Representations of the algebra Uq(sl(2)),
q-orthogonal polynomials and invariants of links,
in V.G. Kac, ed., Infinite dimensional Lie algebras and groups,
Proceedings of the conference held at CIRM, Luminy, Marseille, p. 285,
World Scientific, Singapore (1988).
The q-CG coefficients and q-6j symbols for the rank two quantum
groups were calculated by Joost Slingerland and myself, details can
be found in this paper.
