2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75594A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at generic deformation parameters. Interestingly that finite-dimensional representations of $U_{pq}[sl(2)]$ allow arbitrary complex "spins" (i.e., not necessary they to be integral or half-integral numbers), unlike those in the classical and one-parametric deformation cases.LaTeX, 7 pages, no figure. In v2: Minor corrections; discussions and references added; line spacing reducedQuantum AlgebraHigh Energy Physics - TheoryMathematical PhysicsRepresentation TheoryExactly Solvable and Integrable SystemsQuantum Physics17B37; 81R50text