Embeddings of the Racah Algebra into the Bannai-Ito Algebra

作者：Genest Vincent X^*; Vinet Luc; Zhedanov Alexei

来源：Symmetry Integrability and Geometry-Methods and Applications, 2015, 11: 050.

DOI：10.3842/SIGMA.2015.050

• Bannai-Ito polynomials
• Bannai-Ito algebra
• Racah polynomials
• Racah algebra

Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir operators of the osp(1/2) and su(1, 1) Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai Ito algebras.

• 出版日期2015