Conformally Invariant Powers of Spin Operators on the Sphere

TL;DR

This paper derives explicit formulas for odd-order differential intertwinors acting on spinor-k-form bundles on odd-dimensional spheres, highlighting their relation to Dirac and Rarita-Schwinger operators.

Contribution

It provides the first explicit formulas for all odd-order conformally invariant differential intertwinors on spinor-k-form bundles on spheres.

Findings

Formulas for all odd-order intertwinors derived

Connections to Dirac and Rarita-Schwinger operators established

Enhances understanding of conformal invariance in spin geometry

Abstract

We give explicit formulas for all odd order differential intertwinors on the subbundle of the bundle of spinor-$k$-forms that are annihilated by the Clifford multiplication over the odd dimensional standard sphere. The Dirac and Rarita-Schwinger operators appear in the case of $k=0$ and $k=1$, respectively.