A Fifth Order Conformally Invariant Higher Spin Operator on the Sphere

Abstrakt

We present a new conformally invariant higher order operator on the n-dimensional sphere, acting on functions with values in the representation with highest weight (5/2, 1/2, ..., 1/2). The construction uses the spectrum generating method by Branson, Orsted and Olafsson [6] and is a higher spin analog of the construction of conformally invariant powers of Dirac operators by Liu and Ryan [20] and of the operators on spin-forms constructed recently by Hong [18].

Klíčová slova

• Clifford algebras
• Dirac operators
• representation theory