On the Wikipedia page for restricted representations 


<https://en.wikipedia.org/wiki/Restricted_representation>


there is presented a number of explicit "branching rules". In particular, there is the Weyl's branching rule from U(N) to U(N-1) given in terms of signatures $f\_1 \geq \cdots \geq f\_N$, for $f\_i \in \mathbb{N}$, labelling irreps of U(N). I would guess that this generalises directly to the case of branching from $SU(N)$ to $SU(N-1)$ but cannot find a reference. Can someone suggest a reference?



Weyl's Branching Rule for $SU(N)$-Setting
The question is answered on page 385 of the classical Zhelobenko book


***Compact Lie groups and their representations*** 


for the more general case of $SU(n+m)/SU(n) \times SU(m)$.


