The higher rank q-Bannai-Ito algebra and multivariate (-q)-Racah polynomials

by Hadewijch De Clerc (Ghent University)

Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday April 5, 2019 at 14:30

The q-Bannai-Ito algebra is a quadratic quantum algebra with remarkable properties. It encodes the bispectrality of the (-q)-Racah polynomials, which are the most fundamental orthogonal polynomials of q-hypergeometric type. In this talk, I will explain how this connection can be generalized to multiple variables. We will exploit the Hopf algebraic structure of quantum groups to build a higher rank extension of the q-Bannai-Ito algebra. We will study its action on the discrete series representation of the corresponding quantum group, and identify a class of canonical bases. Several such bases are in duality, in the sense that their overlap coefficients can be expressed as multivariate (-q)-Racah polynomials. The bispectral operators for these polynomials give rise to a discrete realization of the higher rank q-Bannai-Ito algebra.