Valentyna GROZA
National Aviation University,
1 Komarova Ave.,
03058 Kyiv,

Representations of the quantum algebra suq(1,1) and discrete q-ultraspherical polynomials

We derive orthogonality relations for discrete q-ultraspherical polynomials and for their duals by means of operators of discrete series representations of the quantum algebra suq(1,1). Spectra and eigenfunctions of these operators are found explicitly. These eigenfunctions, when normalized, form an orthonormal basis in the representation space.