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1.
The unitary irreducible representations of the u q(2,1) quantum algebra that belong to the intermediate discrete series are considered. The q analog of the Mickelsson-Zhelobenko algebra is developed. Use is made of the U basis corresponding to the reduction u q(2,1) ? u q(2). Explicit formulas for the matrix elements of the generators are obtained in this basis. The projection operator that projects an arbitrary vector onto the extremal vector of the intermediate-series representation is found.  相似文献   

2.
The structure of unitary irreducible representations of the noncompact uq(2, 1) quantum algebra that are related to a negative discrete series is examined. With the aid of projection operators for the suq(2) subalgebra, a q analog of the Gelfand-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 brackets <U∣T>q between the bases associated with the 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, the q Weyl coefficients coincide with the q Racah coefficients for the suq(2) quantum algebra.  相似文献   

3.
We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U q(su(3)). We obtain a very compact general analytic formula for the U q(su(3)) CGCs in terms of the U q(su(2)) Wigner 3nj symbols.  相似文献   

4.
Nonstandard q-deformed algebras U q(so3) and U q(so4), which can be embedded into U q(sl3) and U q(sl4) and are coideals in them, are considered. It is shown how to multiply finite dimensional representations of U q(so3) when q is positive. Homomorphisms from U q(so3) and U q(so4) to the q-oscillator algebras are given. By making use of these homomorphisms, irreducible representations of U q(so3) and U q(so4) for q equal to a root of unity are obtained.  相似文献   

5.
The Borel-Weil (BW) construction for unitary irreps of a compact Lie group is extended to a construction of all unitary irreps of the quantum groupU q(n). Thisq-BW construction uses a recursion procedure forU q(n) in which the fiber of the bundle carries an irrep ofU q(n–1)×U q(1) with sections that are holomorphic functions in the homogeneous spaceU q(n)/U q(n–1)×U q(1). Explicit results are obtained for theU q(n) irreps and for the related isomorphism of quantum group algebras.Supported in part by the National Science Foundation, No. PHY-9008007  相似文献   

6.
The structure of all discrete series of unitary irreducible representations of the U q (u(3, 1)) and U q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U q (u(n, 1)) ⊇ U q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.  相似文献   

7.
We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization ofSU q(2) in terms of aq-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroupU(1) and the remaining cosetSU q(2)/U(1)=CP q(1) consists of aq-oscillator. For unitary quantum groupsSU q (n), the analogous construction results in the quantum projective spaceSU q(n+1)/U q (n)=CP q (n) being identified with then-dimensionalq-oscillator. This yields a nonlinear action of the quantum groupSU q(n+1) on then-dimensionalq-oscillator.  相似文献   

8.
An algebra homomorphism from the nonstandard q-deformed (cyclically symmetric) algebra U q(so3) to the extension Û q(sl2) of the Hopf algebra U q(sl2) is constructed. Not all irreducible representations (IR) of U q(sl2) can be extended to representations of Û q(sl2). Composing the homomorphism with irreducible representations of Û q(sl2) we obtain representations of U q(so3). Not all of these representations of U q(so3) are irreducible. Reducible representations of U q(so3) are decomposed into irreducible components. In this way we obtain all IR of U q(so3) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra so3 when q 1.  相似文献   

9.
Operators of representations corresponding to symmetric elements of theq-deformed algebrasU q (su1,1),U q (so2,1),U q (so3,1),U q (so n ) and representable by Jacobi matrices are studied. Closures of unbounded symmetric operators of representations of the algebrasU q (su1,1) andU q (so2,1) are not selfadjoint operators. For representations of the discrete series their deficiency indices are (1,1). Bounded symmetric operators of these representations are trace class operators or have continuous simple spectra. Eigenvectors of some operators of representations are evaluated explicitly. Coefficients of transition to eigenvectors (overlap coefficients) are given in terms ofq-orthogonal polynomials. It is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq-deformed algebras.  相似文献   

10.
We derive a q-deformed version of the Lorentz algebra by deforming the algebraSL(2,C). The method is based on linear representations of the algebra on the complex quantum spinor space. We find that the generators usually identified withSL q(2,C) generateSU q (2) only. Four additional generators are added which generate Lorentz boosts. The full algebra of all seven generators and their coproduct is presented. We show that in the limitq→1 the generators are those of the classical Lorentz algebra plus an additionalU(1). Thus we have a deformation ofSL(2,CU(1).  相似文献   

11.
《Nuclear Physics B》1998,530(3):641-664
We show that the transfer matrix of the AN−1(1) open spin chair with diagonal boundary fields has the symmetry Uq(SU(l)) × Uq(SU(Nl)) × U(1), as well as a “duality” symmetry which maps lNl. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.  相似文献   

12.
13.
The dually conjugate Hopf algebrasFun p,q (R) andU p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU p,q (R) is extracted. The universal ?-matrix forsFun p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L (±), forU p,q (R) are derived from the ?-matrix.  相似文献   

14.
《Physics letters. [Part B]》1999,461(3):243-247
If the smallness of the mass of the sterile neutrino is to be explained by the see-saw mechanism, the off-diagonal entries of the mass matrix needs to be protected by some symmetry not far above the electroweak scale. We implement see-saw mechanism in a gauge model based on SU(2)qL×SU(2)lL×U(1)qY×U(1)lY un-unified gauge group which breaks to SU(2)L×U(1)Y at the TeV region via a two-step symmetry breaking chain. The right handed diagonal block is tied to the highest scale up to which the un-unification symmetry holds. The sterile neutrino emerges from a quark-lepton mixed representation of the un-unified group.  相似文献   

15.
The Higgs-strahlung production process ppZ′ → ZH is an important process for studying the HZZ′ interaction. We take the B ? L model and the nonuniversal S U(2)1 × S U(2)2 × U(1) Y model as two examples and investigate their correction effects on ZH production at the LHC. Our numerical results show that, considering constraints on these two new physics models, the contributions of the B ? L model to the ZH production cross section are very small, while the S U(1)1 × S U(2)2 × U(1) Y model can generate significant contributions.  相似文献   

16.
General method of spontaneous supersymmetry breaking is developed. On its basis a number of unified lepton models is analyzed. Examples of realistic lepton models based on the groups SU(2) × U(1) and SU(2) × SU(2) × U(1) are considered.  相似文献   

17.
三维各向同性振子的q形变及其波函数   总被引:2,自引:0,他引:2       下载免费PDF全文
潘峰  许佩军 《物理学报》1993,42(6):867-873
详细分析了三维各向同性振子的三种典型的q形变形式。这三种q形变哈密顿量分别具有S3,SUq(2),及Uq(3)对称性。特别地,在第三种情形下给出Uq(3)?SOq′(3)的具体实现。利用形变泛函映射,讨论了q形变振子与经典振子间的关系。  相似文献   

18.
It is shown that the quantum supergroup U q (osp(1/2n)) is essentially isomorphic to the quantum group U -q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.  相似文献   

19.
We give explicit realization of formulae of canonical realization for the quantum enveloping algebrasU q (B 2)~U q (so(5)) andU q (C 2)~U q (sp(4)). In these formulae the generators of the algebra are expressed by means of 3 canonicalq-boson pairs and one auxiliary representation ofU q (gl(2)).  相似文献   

20.
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU q(2) the Green function on the q-Podler's sphere M q = SU q(2)/U(1) is derived. Possible applications are briefly discussed.  相似文献   

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