  The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials
as overlap coefficients in the positive discrete series representations of the
Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to
generalisations of the convolution identities for these polynomials. Using the
Racah coefficients convolution identities for continuous Hahn, Hahn and Jacobi
polynomials are obtained. From the quantised universal enveloping algebra for
su(1,1) convolution identities for the Al-Salam and Chihara polynomials and the
Askey-Wilson polynomials are derived by using the Clebsch-Gordan and Racah
coefficients. For the quantised universal enveloping algebra for su(2) q-Racah
polynomials are interpreted as Clebsch-Gordan coefficients, and the
linearisation coefficients for a two-parameter family of Askey-Wilson
polynomials are derived.
