Degenerations of Sklyanin algebra and Askey-Wilson polynomials

Details Degenerations of Sklyanin algebra and Askey-Wilson polynomials Degenerations of Sklyanin algebra and Askey-Wilson polynomials

1993-03-04

arxiv.org/abs/hep-th/9303026v1

J.Phys. A26 (1993) L635-L640

Physics

High Energy Physics

High Energy Physics - Theory

7 pages

Scientific paper

10.1088/0305-4470/26/15/004

A new trigonometric degeneration of the Sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied. A further contraction gives the standard quantum algebra $U_{q}(sl(2))$. It is shown that the degenerate Sklyanin algebra contains a subalgebra isomorphic to algebra of functions on the quantum sphere $(SU(2)/SO(2))_{q^{1\over2}}$. The diagonalization of general quadratic form in its generators leads in the functional realization to the difference equation for Askey-Wilson polynomials.

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