Ellipticity of Some Higher Order Conformally Invariant Differential Operators

In this article, we prove the ellipticity of higher order conformally invariant differential operators in the higher spin spaces, where functions take values in certain irreducible representations of the spin group in the Euclidean space. We introduce the product formulas for these operators obtained in our previous work to greatly simplify our proofs. In both the bosonic cases and fermionic cases, our product formula enables us to use similar methods as for the higher spin Laplace operator, exploiting the structure of the conformal Lie algebra and branching rules.