Orthogonal Polynomials in Connection with Quantum Groups

This is a survey of interpretations of q hypergeometric orthogonal polynomials on quantum groups The rst half of the paper gives general background on Hopf algebras and quantum groups The emphasis in the rest of the paper is on the SU quantum group An interpretation of little q Jacobi polynomials as matrix elements of its irreducible representations is presented In the last two sections new results by the author on interpretations of Askey Wilson polynomials are discussed NOTE Last modi ed May a few references updated The paper appeared earlier in P Nevai ed Orthogonal Polynomials Theory and Practice NATO ASI Series C Vol Kluwer Academic Publishers PRESENT ADDRESS University of Amsterdam Department of Mathematics Plantage Muider gracht TV Amsterdam The Netherlands email thk fwi uva nl