V. I. Lamansky and Yu. F. Samarin: on the history of relationships

The structure positive of unitary irreducible representations of the noncompact uq(2, 1) quantum algebra that are related to a positive discrete series is examined. With the aid of projection operators for the suq(2) subalgebra, a q-analog of the Gel'fand-Graev formulas is derived in the basis corresponding to the reduction uq(2, 1) → suq(2) × u(1). Projection operators for the suq(1, 1) subalgebra are employed to study the same representations for the reduction uq(2, 1) → u(1) × suq(1, 1). The matrix elements of the generators of the uq(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 suq(2) quantum algebra.

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“…These matrix elements are presented in Table 2(the derivation of these expressions is given in [24].…”

Section: The Remaining Four Non-diagonal Generators Act On the T -Bas...mentioning

confidence: 99%

“…The normalization factor N (T M T ) is determined by formula (69), while the projection operator P T is given by (82). The normalization factor N (sp) for the vectors of T -spin basis is calculated by a method similar to that used for the norm of the vectors of the U -spin basis described in the Appendix (see also [24]). The square of this norm is…”

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confidence: 99%

Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

Smirnov

Kharitonov²

Symmetries in Science XI

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V. I. Lamansky and Yu. F. Samarin: on the history of relationships

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Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

Noncompact Quantum Algebra Uq(2,1): Positive Discrete Series of Irreducible Representations

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