TITLE: 6j symbols of SU(4) at level 4
QUESTION [7 upvotes]: Does anybody know of a reference that gives the (quantum) 6j symbols of SU(4) at level 4?
Alternatively, I know the S-matrix and the fusion rules, in the form
$a \times b = \sum_i N^{ab}_{c_i} c_i$
Is there a simple way to compute all quantum 6j symbols from these?

REPLY [3 votes]: In answer to your second question, no, there is not a simple way to compute $6j$-symbols from the fusion rules and the $S$-matrix.