Symplecton for Uh(sl(2)) and representations of SLh(2)
Abstract
Polynomials of boson creation and annihilation operators which form irreducible tensor operators for Jordanian quantum algebra Uh(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 SLh(2) dual to Uh(sl(2)). As an application of the procedure used to construct h-symplecton, we construct the representation bases of SLh(2) on the quantum h-plane.
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