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.

中文翻译：

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一些高阶共形不变微分算子的椭圆度

在本文中，我们证明了高阶共形不变微分算子在高自旋空间中的椭圆性，其中函数取欧几里得空间中自旋群的某些不可约表示的值。我们引入了我们之前工作中获得的这些运算符的乘积公式，以大大简化我们的证明。在玻色子情况和费米子情况下，我们的乘积公式使我们能够使用与更高自旋拉普拉斯算子类似的方法，利用保形李代数和分支规则的结构。