In the context of branching rules, what is the meaning of the projection matrix, and how/what do I use it for?
For instance, for the branching of $SU\left(5\right)$ under $SU\left(2\right)\times SU\left(3\right)$, I am told that the projection matrix is $$\left(\begin{array}{cccc} 0 & 1 & 1 & 0\\ 1 & 1 & 0 & 0\\ 0 & 0 & 1 & 1 \end{array}\right)$$