The dual pair Pin (2 n) × osp (1  2), the Dirac equation and the BannaiIto algebra
Abstract
The BannaiIto 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 BannaiIto algebra will be traced to the Howe duality which is embodied in the Pin (2 n) × osp (1  2) symmetry of the massless Dirac equation in R^{2n}. Dimensional reduction to R^{n} will provide an alternative to the DiracDunkl equation as a model with BannaiIto symmetry.
 Publication:

Nuclear Physics B
 Pub Date:
 December 2018
 DOI:
 10.1016/j.nuclphysb.2018.10.011
 arXiv:
 arXiv:1810.00130
 Bibcode:
 2018NuPhB.937..226G
 Keywords:

 Mathematical Physics;
 20C35;
 22E70;
 81R12
 EPrint:
 16 pages