The dual pair $Pin(2n)\times\mathfrak{osp}(1|2)$, the Dirac equation and the Bannai-Ito algebra
| Autor: | Gaboriaud, Julien, Vinet, Luc, Vinet, Stéphane, Zhedanov, Alexei |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2018.10.011 |
| Popis: | The Bannai-Ito algebra can be defined as the centralizer of the coproduct embedding of $\mathfrak{osp}(1|2)$ in $\mathfrak{osp}(1|2)^{\otimes n}$. It will be shown that it is also the commutant of a maximal Abelian subalgebra of $\mathfrak{o}(2n)$ 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 $Pin(2n)\times\mathfrak{osp}(1|2)$ symmetry of the massless Dirac equation in $\mathbb{R}^{2n}$. Dimensional reduction to $\mathbb{R}^{n}$ will provide an alternative to the Dirac-Dunkl equation as a model with Bannai-Ito symmetry. Comment: 16 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|