TITLE: Branching laws for $SO(n)$
QUESTION [7 upvotes]: The branching laws for the $SO(n-1)$ as a subgroup of $SO(n)$ are well known and easy to find. See for example the Wikipedia article:
https://en.wikipedia.org/wiki/Restricted_representation#CITEREFMurnaghan1938
I am having trouble finding the next most complicated example, i.e.
$$
SO(n-2) \times SO(2) \subseteq SO(n).
$$
Where can a description of these branching laws be found?
Edit: In particular I would like to know examples of representations of $SO(n-2) \times SO(2)$ which appear with multiplicity $1$ in any branching.

REPLY [2 votes]: check Eastwood-Wolf, branchig of ...., Arxive 0812.0822 math[RT] in this paper you find who to compute branching laws useing LiE.