Symplecton for U_h(sl(2)) and representations of SL_h(2)

Details Symplecton for U_h(sl(2)) and representations of SL_h(2) Symplecton for U_h(sl(2)) and representations of SL_h(2)

1999-07-07

arxiv.org/abs/math/9907038v1

J. Math. Phys. 40 (1999) 5921-5938.

Mathematics

Quantum Algebra

20 pages, LaTeX2e, no figures, to be published in J.Math.Phys

Scientific paper

10.1063/1.533080

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.

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