Representations and classification of the compact quantum groups Uq(2) for complex deformation parameters

In this paper, we obtain a complete list of inequivalent irreducible representations the compact quantum group [Formula: see text] for nonzero complex deformation parameters text], which are not roots unity. The matrix coefficients these described in terms little text]-Jacobi polynomials. Haar state is shown to be faithful and an orthonormal basis obtained. Thus, have explicit description Peter–Weyl decomposition text]. As application, discuss Fourier transform establish Plancherel formula. We also describe tensor product two into components. Finally, classify