We study the massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space. The Casimir operators are constructed and their eigenvalues are found. It is shown that the finite spin (helicity) representation is defined by two integer or half-integer numbers while the infinite spin representation is defined by the real parameter ${\mu }^2$ and one integer or half-integer number.

中文翻译：

---

庞加莱群在六个维度上的无质量有限和无限自旋表示

我们研究了六维Minkowski空间中庞加莱群的无质量不可约表示。构造卡西米尔算子并找到其特征值。结果表明，有限自旋（螺旋）表示由两个整数或半整数定义，而无限自旋表示由实数参数定义${\mu }^2$ 和一个整数或半整数。