An Invitation to Matrix Valued Spherical Functions: Linearization of   Products in the Case of the Complex Projective Space $P_2({\mathbb C})$
  We present a friendly introduction to the very detailed results in [9,10,11] and as an illustration we discuss here the issue of {\em linearization of products}. We find some interesting new phenomena. 
F. A. Grunbaum, I. Pacharoni, and J. Tirao