Title: Finite bivariate Tratnik functions
| Speaker: |
Meri Zaimi |
| Affiliation: |
Perimeter Institute for Theoretical Physics |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: In the context of algebraic combinatorics, P- and Q-polynomial association schemes are important objects and are closely related to distance-regular graphs. The polynomials appearing in these structures are classified by Leonard's theorem, and they belong to the discrete part of the (q-)Askey scheme. Relatively recently, the notions of P- and Q-polynomial association schemes as well as of distance-regular graphs have been generalized to the multivariate case. There is however no multivariate analog of Leonard's theorem. With the purpose of progressing in that direction, I will discuss ongoing work concerning certain finite families of bivariate functions, said of Tratnik type, which are expressed as an intricate product of univariate polynomials of the (q-)Askey scheme. The goal is to classify such functions which satisfy some generalized bispectral properties, that is, two recurrence relations and two (q-)difference equations of certain types.