| Popis: |
The structure positive of unitary irreducible representations of the noncompact u q (2,1) quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the su q (2) subalgebra, a q-analog of the Gel’fand-Graev formulas is derived in the basis corresponding to the reduction u q (2,1) → su q (2)×u(1). Projection operators for the su q (1, 1) subalgebra are employed to study the same representations for the reduction u q (2, 1) → u(1)×su q (1, 1). The matrix elements of the generators of the u q (2,1) algebra are computed in this new basis. A general analytic expression for an element of the transformation bracket 〈U‖T〉 q between the bases associated with above two reductions (the elements of this matrix are referred to as q-Weyl coefficients) is obtained for a general case where the deformation parameter q is not equal to a root of unity. It is shown explicitly that, apart from a phase, q-Weyl coefficients coincide with the q-Racah coefficients for the su q (2) quantum algebra. |
