About non-linear realization of quantumSL q(2, R) group

Using the Fronsdal-Galindo formula for the exponential mapping from the quantum algebra U p,q (gl(2)) to the quantum group GL p,q (2), we show how the (2j+1)-dimensional representations of GL p,q (2) can be obtained by 'exponentiating' the well-known (2j + 1)-dimensional representations of U p,q (gl(2)) for j = 1, corresponds to the defining 2-dimensional T -matrix. The earlier results on the finite-dimensional representations of GL q (2) and SL q (2) (or SU q (2)) are obtained when p = q. Representations of Uq ,q (2) (q ∈ C\R and U q (2) (q ∈ R\{0}) are also considered. The structure of the Clebsch-Gordan matrix for U p,q (gl (2)) is studied. The same Clebsch-Gordan coefficients are applicable in the reduction of the direct product representations of the quantum group GL p,q (2).

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“…Akulov et al [27] have considered the differential calculus of the group parameter space for SL q (2) and studied a related field theory model.…”

Section: Resultsmentioning

confidence: 99%

Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))

Jagannathan

Jeugt

1995

J. Phys. A: Math. Gen.

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“…Recently Fronsdal and Galindo [1] have studied the duality structure relating F un p,q (GL(2)) and U p,q (gl( 2)) (see also [2,3] for some aspects of a similar approach to F un q (GL(2)) and F un q (SL(2)) ) wherein the transfer matrix T gets replaced by the representation-independent universal T -matrix. The universal T -matrix, identified with the dual form…”

Section: Introductionmentioning

confidence: 99%

On the hopf structure of U p,q (gl(1?1)) and the universal T-matrix of fun p,q (GL(1?1))

Chakrabarti

Jagannathan

1996

Letters in Mathematical Physics

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Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys. 27 (1993) 57) for studying the Hopf duality between the quantum algebras F un p,q (GL(2)) and U p,q (gl(2)), the Hopf structure of U p,q (gl(1|1)), dual to F un p,q (GL(1|1)), is derived and the corresponding universal T -matrix of F un p,q (GL(1|1)), embodying the suitably modified exponential relationship U p,q (gl(1|1)) → F un p,q (GL(1|1)), is obtained.

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“…For any elements g, g ′ ∈ SL q (2, R) element g ′′ = g ′ g will belong SLq(2, R) if a k ′ a l = a l a k ′ . In the Gauss decomposition [2] g = 1 ϕ − 0 1…”

mentioning

confidence: 99%

“…between variation dg and g define the type of the differential calculus. The left-invariant differential calculus [3] on the GL q (2, C) group, matched with the differential calculi on the SL q (2, C) subgroup and on the Borel subgroups B L (C), B U (C), was constructed in [4,5]. Let ω = g −1 dg is the left differential Kartan 1-form…”

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confidence: 99%

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0) and infinitesimal transformations

Gershun¹

Supersymmetry and Quantum Field Theory

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arXiv:q-alg/9709022v1 15 Sep 1997 σ -models on the quantum group manifolds SL q (2, R), SL q (2, R)/U h (1), C q (2|0) and infinitesimal transformations. V.D. GershunKharkov Institute of Physics and Technology, 310108, Kharkov, UkraineThe differential and variational calculus on the SL q (2, R) group is constructed. The spontaneous breaking symmetry in the WZNW model with SL q (2, R) quantum group symmetry and in the σ-models with SL q (2, R)/U h (1) ,C q (2|0) quantum group symmetry is considered. The Lagrangian formalism over the quantum group manifolds is discussed. The classical solution of C q (2|0) σ-model is obtained.

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About non-linear realization of quantumSL q(2, R) group

Cited by 3 publications

References 6 publications

Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))

Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))

On the hopf structure of U p,q (gl(1?1)) and the universal T-matrix of fun p,q (GL(1?1))

0) and infinitesimal transformations

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About non-linear realization of quantumSL q(2, R) group

Cited by 3 publications

References 6 publications

Finite-dimensional representations of the quantum group GLp,q(2) using the exponential map from Up,q(gl(2))

Finite-dimensional representations of the quantum group GLp,q(2) using the exponential map from Up,q(gl(2))

On the hopf structure of U p,q (gl(1?1)) and the universal T-matrix of fun p,q (GL(1?1))

0) and infinitesimal transformations

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Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))

Finite-dimensional representations of the quantum group GL_p,q(2) using the exponential map from U_p,q(gl(2))