论文标题
一般的RACAH代数为伪系统上通用系统的对称代数-Spheres
The general Racah algebra as the symmetry algebra of generic systems on pseudo--spheres
论文作者
论文摘要
我们表征了对应于均质空间$ so（p，q+1）/so（p，q）$的伪弹丸上通用共聚系统的对称代数，其中$ p+q = {\ cal n} $，$ {\ cal n} \ in \ mathbb n $。我们表明，该代数独立于该度量的签名$（p，q+1）$，并且与racah代数$ {\ cal r}（{\ cal n} +1）$相同。通过daskaloyannis方法从$ {\ cal r}（{\ cal n} +1）$获得的频谱取决于可以与签名关联的未确定标志。对于$（2,1）/so（2）$和$ SO（3）/SO（2）$，明确处理了两个示例，其中表明它们通过变量分离而获得的spectrum与对称spectrum spectrum的特定符号的特定符号的特定符号相一致，以符合对称的algebra $ a = algebra $的特定签名。
We characterize the symmetry algebra of the generic superintegrable system on a pseudo-sphere corresponding to the homogeneous space $SO(p,q+1)/SO(p,q)$ where $p+q={\cal N}$, ${\cal N}\in\mathbb N$. We show that this algebra is independent of the signature $(p,q+1)$ of the metric and that it is the same as the Racah algebra ${\cal R}({\cal N}+1)$. The spectrum obtained from ${\cal R}({\cal N}+1)$ via the Daskaloyannis method depends on undetermined signs that can be associated to the signatures. Two examples are worked out explicitly for the cases $SO(2,1)/SO(2)$ and $SO(3)/SO(2)$ where it is shown that their spectrum obtained by means of separation of variables coincide with particular choices of the signs corresponding to the specific signatures of the spectrum for the symmetry algebra ${\cal R}(3)$.
