Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
However, since we have a Gelfand-pair, the trivial representation of $SO(n-2) \times SO(2)$ can appear only once in the decomposition of any $SO(n)$-module.
@Peter: Thank you a lot for reference! It is somewhat technical for me unfortunately. Can we see from Proctor's results, that for example, when the branchings are multiplicity free? I.e. are branching always multiplicity free, or maybe just for the fundamental representations?
