The dual pair Pin(2n)×osp(1|2), the Dirac equation and the Bannai–Ito algebra

@article{Gaboriaud2018TheDP,
  title={The dual pair Pin(2n)×osp(1|2), the Dirac equation and the Bannai–Ito algebra},
  author={Julien Gaboriaud and Luc Vinet and St'ephane Vinet and Alexei S. Zhedanov},
  journal={Nuclear Physics B},
  year={2018}
}
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… Expand
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