Dynamical quantum groups were recently introduced by Etingof and Varchenko as
an algebraic framework for studying the dynamical Yang-Baxter equation, which
is precisely the Yang-Baxter equation satisfied by 6j-symbols. We investigate
one of the simplest examples, generalizing the standard SU(2) quantum group.
The matrix elements for its corepresentations are identified with Askey-Wilson
polynomials, and the Haar measure with the Askey-Wilson measure. The discrete
orthogonality of the matrix elements yield the orthogonality of q-Racah
polynomials (or quantum 6j-symbols). The Clebsch-Gordan coefficients for
representations and corepresentations are also identified with q-Racah
polynomials. This results in new algebraic proofs of the Biedenharn-Elliott
identity satisfied by quantum 6j-symbols.Comment: 51 pages; minor correction
