论文标题
3D Dirac-Dunkl操作员的特殊对称代数
An exceptional symmetry algebra for the 3D Dirac-Dunkl operator
论文作者
论文摘要
我们启动对与特殊根系$ G_2 $的Weyl组相关的3D Dirac-Dunkl操作员对称代数的研究。对于此对称代数，我们既给出抽象的定义又有明确的实现。然后，我们使用中间结果来构建梯子运算符，我们证明了与在三维空间上作用于任意有限反射组相关的Dirac-Dunkl对称代数。
We initiate the study of an algebra of symmetries for the 3D Dirac-Dunkl operator associated with the Weyl group of the exceptional root system $G_2$. For this symmetry algebra, we give both an abstract definition and an explicit realisation. We then construct ladder operators, using an intermediate result we prove for the Dirac-Dunkl symmetry algebra associated with arbitrary finite reflection group acting on a three-dimensional space.
