The dual pair Pin (2n) x osp(1 vertical bar 2), the Dirac equation and the Bannai-Ito algebra
The dual pair Pin (2n) x osp(1 vertical bar 2), the Dirac equation and the Bannai-Ito algebra
复制标题
对偶对 Pin (2n) x osp(1 竖条 2)、狄拉克方程和 Bannai-Ito 代数
DOI：
10.1016/j.nuclphysb.2018.10.011
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发表时间：
2018
影响因子：
2.8
通讯作者：
Zhedanov Alexei
中科院分区：
文献类型：
--
作者：
Gaboriaud Julien;Vinet Luc;Vinet Stephane;Zhedanov Alexei
摘要 Bannai-Ito 代数可以定义为 osp (1| 2) 在 osp (1| 2)⊗ n 中的余积嵌入的中心化子。将证明它也是旋量表示中 o (2 n) 的最大阿贝尔子代数的交换子，并且将出现 Racah 代数在该交换子中的嵌入。 Bannai-Ito 代数的两幅图像之间的联系将追溯到豪对偶性，豪对偶性体现在 R 2 n 中无质量狄拉克方程的 P i n (2 n)× osp (1| 2) 对称性中。降维至 R n 将提供 Dirac-Dunkl 方程的替代方案，作为具有 Bannai-Ito 对称性的模型。
Abstract The Bannai–Ito algebra can be defined as the centralizer of the coproduct embedding of osp (1| 2) in osp (1| 2)⊗ n. It will be shown that it is also the commutant of a maximal Abelian subalgebra of o (2 n) in a spinorial representation and an embedding of the Racah algebra in this commutant will emerge. The connection between the two pictures for the Bannai–Ito algebra will be traced to the Howe duality which is embodied in the P i n (2 n)× osp (1| 2) symmetry of the massless Dirac equation in R 2 n. Dimensional reduction to R n will provide an alternative to the Dirac–Dunkl equation as a model with Bannai–Ito symmetry.