Conformally invariant higher order higher spin operators on the sphere

Abstrakt

We study conformally invariant differential operators on functions valued in Spin(n)-representations with half-integral highest weights (higher spin representations) on the sphere. We show that for most of these representations there is a unique such operator of arbitrary odd order, and construct new examples for the highest weight (5/2, 1/2, ... , 1/2), using the spectrum generating method by Branson, Orsted and Olafsson [6].

These operators are higher spin analogs of the conformally invariant powers of Dirac operator first constructed by Liu and Ryan [21].

Klíčová slova

• Clifford algebras
• Dirac operators
• conformal geometry