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

Nguyen Anh Ky·Nguyen Thi Hong Van
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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.

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Nguyen Anh Ky, Nguyen Thi Hong Van. 2005-07-15. A two-parametric deformation of U[sl(2)], its representations and complex "spin". https://arxiv.org/abs/math/0506539

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