2 7 Ju n 20 05 A two - parametric deformation of U [ sl ( 2 ) ] , its representations and complex ” spin ”

A two-parametric deformation of U [sl(2)], its representations and complex " spin " Abstract A 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.