A branching law for the symplectic groups (Q2522114)

Let \(\mathrm{US}_p(\mu)\) be the intersection of the symplectic and unitary groups of degree \(2\mu\) over the complex field. The irreducible continuous representations of \(\mathrm{US}_p(\mu)\) can be denoted by \({}^\mu \omega_{f_1\cdots f_\mu}\), where the \(f_1,\ldots,f_\mu\) are integers such that \(f_1 \ge \dots \ge f_\mu \ge 0\). A determinantal formula is given for the multiplicity \(R_{g_1\cdots g_{\mu-1}}^{f_1\cdots f_\mu}\) of \({}^{\mu-1} \omega_{g_1\cdots g_{\mu-1}}\) in the restriction of \({}^\mu \omega_{f_1\cdots f_\mu}\) to the subgroup of \(\mathrm{US}_p(\mu)\) leaving the last two basis elements fixed. This is equal to a certain multiplicity defined in a similar way for the unitary groups.