Geoffroy Bergeron, CRM

$SU_q(3)$ corepresentations and multivariate q-Krawtchouk polynomials

In this talk, an algebraic interpretation of the multivariate quantum $q$-Krawtchouk polynomials in terms of quantum groups will be given. I will begin by reviewing the $SU_q(3)$ quantum group Hopf algebra and present how the symmetric corepresentations are constructed. Then, by first establishing the unitarity of these corepresentations, I will demonstrate that their matrix elements can be expressed in terms of the bivariate $q$-Krawtchouk polynomials. Finally, some applications of this quantum group interpretation will be briefly presented. (This is joint work with Erik Koelink and Luc Vinet.)