Abstract
Explicit realization of SUq(2) algebra is found in terms of operators acting on a two-dimensional sphere and depending on ( theta , phi ) variables. The corresponding eigenfunctions ('spherical q-functions') appear to be a q-generalization of ordinary Legendre polynomials. The recurrence relations and explicit expression in terms of Askey-Wilson polynomials are obtained. The weight function of these polynomials is expressed via double-periodic elliptic functions.
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