A higher rank Racah algebra and the Z2n Laplace–Dunkl operator
A higher rank Racah algebra and the Z2n Laplace–Dunkl operator
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DOI：
10.1088/1751-8121/aa9756
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
H. De Bie;Vincent X. Genest;W. van de Vijver;L. Vinet
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文献类型：
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作者：
H. De Bie;Vincent X. Genest;W. van de Vijver;L. Vinet
作为与Z2n根系统相关的Laplace-Dunkl算子的对称代数，得到了（秩1）Racah代数的高阶概化。这个代数也是n球上一般超可积模型的不变性代数。利用Cauchy-Kovalevskaia定理构造了Dunkl谐波的基。这些基由高阶Racah代数的标记阿贝尔子代数的联合特征函数组成。给出了一种计算这些基之间的连接系数和对称对这些基的作用的表达式。
A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry algebra of the Laplace–Dunkl operator associated to the Z2n root system. This algebra is also the invariance algebra of the generic superintegrable model on the n-sphere. Bases of Dunkl harmonics are constructed explicitly using a Cauchy–Kovalevskaia theorem. These bases consist of joint eigenfunctions of labelling Abelian subalgebras of the higher rank Racah algebra. A method to obtain expressions for both the connection coefficients between these bases and the action of the symmetries on these bases is presented.