A generalization of the Cartan-Helgason theorem for Riemannian symmetric spaces of rank one (Q2496571)

From the author's abstract: ''Let \(U/K\) be a compact Riemannian symmetric space with \(U\) simply connected and \(K\) connected. If \(U/K\) has rank one, then \(\delta | _K\) contains \(\tau\) if and only if \(\tau | _M\) contains \(\sigma\) and \(\mu \in \mu_{\sigma,\tau}+\Lambda_{sph}\), where \(\Lambda_{sph}\) is the set of highest restricted spherical weights and \(\mu_{\sigma,\tau}\) is a suitable element. In this paper we obtain an explicit formula for this element in case of \(U/K = S^n, P^n(C), P^n(H)\). This gives a generalization of the Cartan-Helgason theorem to arbitrary \(K\)-types on these rank one symmetric spaces.''