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W2897218430 abstract "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 $Pin(2n)timesmathfrak{osp}(1|2)$ 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." @default.
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W2897218430 date "2018-12-01" @default.
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W2897218430 doi "https://doi.org/10.1016/j.nuclphysb.2018.10.011" @default.
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