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  • Artikel  (19)
  • 17B37  (19)
  • 2005-2009
  • 1990-1994  (19)
  • 1994  (19)
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  • Artikel  (19)
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  • 2005-2009
  • 1990-1994  (19)
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  • Physik  (18)
  • 1
    Digitale Medien
    Digitale Medien
    Quantum homogeneous spaces, duality and quantum 2-spheres (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 291-315 
    Details
    ISSN: 1572-9168
    Schlagwort(e): 16W30 ; 17B37 ; 22E99 ; quantum groups ; quantum homogeneous spaces ; coaction ; dual Hopf algebras ; two-sided coideals ; infinitesimal invariance ; quantum SU(2) ; sl(2) quantized universal enveloping algebra ; quantum 2-spheres
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01278478
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  • 2
    Digitale Medien
    Digitale Medien
    An elliptic quantum algebra for $$\widehat{s1}_2 $$ 2 (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 259-268 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 82A67
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract An elliptic deformation of $$\widehat{s1}_2 $$ is proposed. Our presentation of the algebra is based on the relationRLL = LLR *, whereR andR * are eight-vertexR-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation ofR * is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750668
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  • 3
    Digitale Medien
    Digitale Medien
    On affine yangians (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 269-274 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50 ; 82B23
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A Yangian $$Y(\widetilde{sl}(2))$$ , a deformation of the universal enveloping algebra of the two-dimensional loop algebra sl(2) ⊗C [t −1,t;u], is constructed. This deformation is an analogue of a Yangian which was constructed by V. Drinfeld for any simple Lie algebra. The PBW theorem for $$Y(\widetilde{sl}(2))$$ is proved and some representations are constructed. Like usual Yangians, $$Y(\widetilde{sl}(2))$$ possesses a one-dimensional group of auto- morphisms and at zero level - a two-dimensional group of automorphisms. This observation allows one to conjecture that the representation theory of $$Y(\widetilde{sl}(2))$$ should give rise to new solutions of QYBE. Yangians of other affine algebras can be constructed similarly and they enjoy similar properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00761137
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  • 4
    Digitale Medien
    Digitale Medien
    Heisenberg realization for U q (sl n ) on the flag manifold (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 35-43 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 16S32 ; 81R10 ; 33D80
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We give the Heisenberg realization for the quantum algebra U q (sl n ), which is written by theq-difference operator on the flag manifold. We construct it from the action of U q (sl n ) on theq-symmetric algebraA q (Mat n ) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U q $$(\widehat{s1_n })$$ [2].
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00761420
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  • 5
    Digitale Medien
    Digitale Medien
    Small representations of quantum affine algebras (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 131-145 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We characterize the finite-dimensional representations of the quantum affine algebra U q ( $$\widehat{sl}$$ n+1) (whereq ∈ ℂ× is not a root of unity) which are irreducible as representations of U q (sl n+1). We call such representations ‘small’. In 1986, Jimbo defined a family of homomorphismsev a from U q (sl n+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ∈ ℂ·. A second family,ev a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U q ( $$\widehat{sl}$$ n+1) is obtained by pulling back an irreducible representation of U q (sl n+1) byev a orev a for somea ∈ ℂ·.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00939701
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  • 6
    Digitale Medien
    Digitale Medien
    Free boson representation of $$U_q (\widehat{sl}_3 )$$ (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 207-216 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 16W30 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A representation of the quantum affine algebra $$U_q (\widehat{sl}_3 )$$ of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq → 1 limit. The analogues of the screening currents are also obtained. They commute with the action of $$U_q (\widehat{sl}_3 )$$ modulo total differences of some fields.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00805853
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  • 7
    Digitale Medien
    Digitale Medien
    Algebraic deformation program on minimal nilpotent orbit (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 241-250 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B35 ; 17B37 ; 22E46
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We construct an algebraic star product on the minimal nilpotent coadjoint orbit of a simple complex Lie group with a Lie algebra which is not of typeA n. According to the deformation program, we study the representations of the Lie algebra associated to this orbit.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00805856
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  • 8
    Digitale Medien
    Digitale Medien
    Quantized affine Lie algebras and diagonalization of braid generators (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 267-277 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Let U q $$(\hat{\mathcal{G}})$$ be a quantized affine Lie algebra. It is proven that the universal R-matrix R of U q $$(\hat{\mathcal{G}})$$ satisfies the celebrated conjugation relationR + =TR withT the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight U q $$(\hat{\mathcal{G}})$$ -module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin and Gould forms to the present affine case. Casimir invariants are constructed and their eigenvalues computed by means of the spectral decomposition formula. As a by-product, an interesting identity is found.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00751063
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  • 9
    Digitale Medien
    Digitale Medien
    On aq-deformation of the discrete Painlevé I equation andq-orthogonal polynomials (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 327-336 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 33D45 ; 39A70 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We present aq-analog of the discrete Painlevé I equation, and a special realization of it in terms ofq-orthogonal polynomials.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00751068
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  • 10
    Digitale Medien
    Digitale Medien
    Metric on quantum spaces (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 35-39 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 46L87 ; 81R50 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract We introduce the analogue of the metric tensor in the case ofq-deformed differential calculus. We analyse the consequences of the existence of the metric, showing that this enforces severe restrictions on the parameters of the theory. We discuss in detail examples of the Manin plane and theq-deformation of SU(2). Finally we touch the topic of relations with Connes' approach.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00751169
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  • 11
    Digitale Medien
    Digitale Medien
    Casimir invariants for quantized affine Lie algebras (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 77-83 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00751173
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  • 12
    Digitale Medien
    Digitale Medien
    Quantum affine algebras and universalR-matrix with spectral parameter (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 101-110 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A 1) and U q (A 2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A 2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750144
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  • 13
    Digitale Medien
    Digitale Medien
    Quantization of U q [so(2n + 1)] with deformed para-Fermi operators (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 151-157 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 16W30 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract The observation thatn pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n + 1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. With this background U q [so(2n + 1)] and its ‘Cartan-Weyl’ generators are written down entirely in terms of deformed para-Fermi operators.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750149
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  • 14
    Digitale Medien
    Digitale Medien
    R-matrix method for Heisenberg quantum groups (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 159-166 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 81R50 ; 70H05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract TheR-matrix method is systematically applied to get several Heisenberg quantum groups depending on two or three parameters. It turns out that the associatedR-matrices have to verify a weaker form of the QYBE. Only for particular cases of quantum groups, we can imposeR to be a solution of the QYBE. The corresponding quantum Heisenberg Lie algebras are obtained by duality.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750150
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  • 15
    Digitale Medien
    Digitale Medien
    Poisson structures on the Lorentz group (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 11-23 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 22E46 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Poisson-Lie structures on the Lorentz group are completely classified. A method applicable to an arbitrary semisimple complex Lie group (treated as real) is developed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00761120
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  • 16
    Digitale Medien
    Digitale Medien
    Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 25-36 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 17B37 ; 46L87 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract Covariant differential calculi on the quantum space $$\mathfrak{X}_{q\lambda \rho }$$ for the quantum group SL q (2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de j of the generators of $$\mathfrak{X}_{q\lambda \rho }$$ form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), ∞ there exists a unique differential calculus with the above properties on the space $$\mathfrak{X}_{q\lambda \rho }$$ which corresponds to Podles' quantum sphereS qc /2 .
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00761121
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  • 17
    Digitale Medien
    Digitale Medien
    Representation theory of quantized poincaré algebra. tensor operators and their applications to one-particle systems (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 85-101 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R50 ; 16W30 ; 17B37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract A representation theory of the quantized Poincaré (κ-Poincaré) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the nondeformed Poincaré algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed. These results are used for the construction of someq-relativistic equations. The Wigner-Eckart theorem for QPA is proven.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00739419
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  • 18
    Digitale Medien
    Digitale Medien
    Diagonalization of the braid generator on unitary irreps of quantum supergroups (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 231-240 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 81R10 ; 17B37 ; 16W30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract It is shown that the braid generator σ associated with the universalR-matrix is diagonalizable on all unitary representations of quantum supergroups. An example is considered using U q (gl(2|1)) and a family of eight-dimensional typical representations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750665
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  • 19
    Digitale Medien
    Digitale Medien
    Left regular representation and contraction of sl q (2) to e q (2) (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 249-258 
    Details
    ISSN: 1573-0530
    Schlagwort(e): 16W30 ; 17B37 ; 81R10 ; 81R50
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract The left regular representation of the quantum algebras sl q (2) and e q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00750667
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