Symplecton for U_h(sl(2)) and representations of SL_h(2)
Quantum Algebra
2009-10-31 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/9907038,
title = {Symplecton for U_h(sl(2)) and representations of SL_h(2)},
author = {N. Aizawa},
journal= {arXiv preprint arXiv:math/9907038},
year = {2009}
}
Comments
20 pages, LaTeX2e, no figures, to be published in J.Math.Phys