$\mathfrak{osp}(1,2)$ and generalized Bannai-Ito algebras

vincent X. Genest, Luc Lapointe, Luc Vinet

Generalizations of the (rank 1) Bannai-Ito algebra are obtained from a refinement of the grade involution of the Lie super algebra $\mathfrak{osp}(1,2)$. A hyperoctahedral extensio…