Symplecton for U_h(sl(2)) and representations of SL_h(2)
arXiv:math/9907038 · doi:10.1063/1.533080
Abstract
Polynomials of boson creation and annihilation operators which form irreducible tensor operators for Jordanian quantum algebra U_h(sl(2)), called h-symplecton, are introduced and their properties are investigated. It is shown that many properties of symplecton for Lie algebra sl(2) are extended to h-symplecton. The h-symplecton is also a basis of irreducible representation of SL_h(2) dual to U_h(sl(2)). As an application of the procedure used to construct h-symplecton, we construct the representation bases of SL_h(2) on the quantum h-plane.
20 pages, LaTeX2e, no figures, to be published in J.Math.Phys
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