Intertwinors on Functions over the Product of Spheres

TL;DR

This paper derives explicit formulas for intertwinors on scalar functions over product spheres, providing an alternative proof for known conformally invariant differential operators using spectrum generating techniques.

Contribution

It introduces explicit formulas for intertwinors on product spheres and offers a new proof for existing conformally invariant differential operators.

Findings

Explicit formulas for intertwinors derived

Alternative proof for conformally invariant operators

Utilizes spectrum generating technique

Abstract

We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of the even order conformally invariant differential operator formulas obtained earlier by T. Branson and the present author.