FoCM 2014 conference

Workshop C5 - Special Functions and Orthogonal Polynomials

December 20, 16:00 ~ 16:30 - Room A21

## A $q$-generalization of the Bannai--Ito polynomials and the quantum superalgebra $\mathfrak{osp}_{q}(1|2)$

### Luc Vinet

### Université de Montréal, Canada - luc.vinet@umontreal.ca

A $q$-generalization of the Bannai--Ito polynomials is presented. These basic polynomials are obtained by considering the Racah problem for the quantum superalgebra $\mathfrak{osp}_{q}(1|2)$. A quantum deformation of the Bannai--Ito algebra is realized by the intermediate Casimir operators entering in the Racah problem. The relation between the $q$-analogs of the Bannai--Ito polynomials and the $q$-Racah/Askey-Wilson polynomials is discussed.

Joint work with Vincent X. Genest (CRM) and Alexei Zhedanov (Donetsk).