Let $\pi_m$, $m \geq 0$, be the unitary irreps of $\mathrm{SU}(2)$. The Clebsch--Gordan decomposition then gives that $$ \pi_m \otimes \pi_n = \bigoplus_{k=0}^{\min(m,n)}\pi_{m+n-2k}.$$ But suppose I want to think of this decomposition as matrices. Evaluating at a point $x \in \mathrm{SU}(2)$, on the left I have $$ (\pi_m(x))_{ij} (\pi_n(x))_{pq}.$$ How do the indices $i,j$ and $p,q$ correspond to the indices on the big matrix on the right?

Let $\pi_m$, $m \geq 0$, be the unitary irreps of $\mathrm{SU}(2)$. The Clebsch–Gordan decomposition then gives that $$ \pi_m \otimes \pi_n = \bigoplus_{k=0}^{\min(m,n)}\pi_{m+n-2k}.$$ But suppose I want to think of this decomposition as matrices. Evaluating at a point $x \in \mathrm{SU}(2)$, on the left I have $$ (\pi_m(x))_{ij} (\pi_n(x))_{pq}.$$ How do the indices $i$, $j$ and $p$, $q$ correspond to the indices on the big matrix on the right?