An Invitation to Matrix Valued Spherical Functions: Linearization of Products in the Case of the Complex Projective Space $P_2({\mathbb C})$

TL;DR

This paper introduces matrix-valued spherical functions, focusing on linearization of products in the context of complex projective space, revealing new phenomena and providing an accessible overview of detailed prior results.

Contribution

It offers a friendly introduction to matrix-valued spherical functions and explores new phenomena in the linearization of products for complex projective space.

Findings

Identification of new phenomena in product linearization

Illustration of detailed prior results in a simplified manner

Application to complex projective space P_2(C)

Abstract

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.