Noncompact u q(2, 1) quantum algebra: Discrete series of highest weight irreducible representations

Smirnov, Yu.F.; Kharitonov, Yu.I.; Asherova, R.M.

doi:10.1134/1.1619503

Cited by 1 publication

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been explicitly shown that these q-Weyl coefficients are equivalent (apart from phase factor ) to specific q-Racah coefficient for the u q (2) algebra or are proportional to the q-6j symbol for the su q (2) algebra. The negative discrete series was discussed by us in [26]. The intermediate discrete series requires a dedicated investigation, and this will be done in our further publication.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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

Smirnov

Kharitonov²

Symmetries in Science XI

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

“…The structure of the U -basis vectors is described by formulas (19)- (26). Here, we use the transformation properties of the "noncompact" generators under Hermitian conjugation and the properties of projection operator P U :…”

Section: Resultsmentioning

confidence: 99%

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

Smirnov

Kharitonov²

Symmetries in Science XI

Self Cite

View full text Add to dashboard Cite

show abstract

Noncompact u q(2, 1) quantum algebra: Discrete series of highest weight irreducible representations

Cited by 1 publication

References 4 publications

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

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

Contact Info

Product

Resources

About