Let $T$ be the "fundamental" representation (I mean the one in which the matrices representing the group elements are simply themselves) of $SU(N)$ group. I have
\begin{pmatrix} SU(N-1)& 0\\ 0& 1 \end{pmatrix}
where $SU(N-1)$ is subgroup of $SU(N)$.
Can I decompose representation $T$ of $SU(N)$ to irreducible representations of $SU(N-1)$? If yes, can you explain me how to do it?