Intertwinors on Differential Forms over the Product of Spheres

TL;DR

This paper derives explicit formulas for intertwinors on differential forms over product spheres with a pseudo-Riemannian metric, leading to the construction of conformally invariant differential operators of all even orders.

Contribution

It provides explicit formulas for intertwinors on differential forms over product spheres and constructs all even-order conformally invariant differential operators.

Findings

Explicit formulas for intertwinors on differential forms

Construction of all even-order conformally invariant operators

Application to pseudo-Riemannian product spheres

Abstract

We give explicit formulas for the intertwinors on the differential form bundles over $S^{p-1} \times S^{q-1}$ with the standard pseudo-Riemannian metric $g=-g_{{}_{S^{p-1}}}+g_{{}_{S^{q-1}}}$ of signature $(p-1,q-1)$. As a special case, we construct conformally invariant differential operators of all even orders.