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

Details 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"

2005-06-27

arxiv.org/abs/math/0506539v2

Mathematics

Quantum Algebra

LaTeX, 7 pages, no figure. In v2: Minor corrections; discussions and references added; line spacing reduced

Scientific paper

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.

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