Bannai-Ito algebras and the $osp(1,2)$ superalgebra

Abstract

The Bannai-Ito algebra $B(n)$ of rank $(n-2)$ is defined as the algebra generated by the Casimir operators arising in the $n$-fold tensor product of the $osp(1,2)$ superalgebra. The structure relations are presented and representations in bases determined by maximal Abelian subalgebras are discussed. Comments on realizations as symmetry algebras of physical models are offered.

Contribution to the proceedings of Group 31, Rio de Janeiro, June 2016; based on a talk by Luc Vinet at this conference; slightly revised version