In his paper *Index for subfactors* [Invent. Math., vol. 72 (1983), pp. 1-26], Vaughan Jones proved his remarkable **index rigidity theorem**, i.e., the fact that the possible index values for a (type II$_1$) subfactor are precisely those in the set
$$
\{4\cos(\pi/n)^{2}\,:\,n\geq 3\}\cup [4,+\infty].
$$
In particular, he constructed a subfactor with index $\alpha$ for each value $\alpha$ in the "discrete series" $\{4\cos(\pi/n)^{2}\,:\,n\geq 3\}$.
In section 2.4 of the report https://www.birs.ca/workshops/2014/14w5083/report14w5083.pdf it is stated, with reference to these subfactors, that

The subfactors arising from the discrete series in his [Vaughan Jones'] article come from SU$_q$(2) at a root of unity.

I would like to know precisely what is meant by this statement.