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  • Springer  (25)
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  • 1
    Electronic Resource
    Electronic Resource
    q-Difference intertwining operators and q-conformal invariant equations (1996)
    Springer
    Acta applicandae mathematicae 44 (1996), S. 81-116 
    Details
    ISSN: 1572-9036
    Keywords: 17B37 ; 81R50 ; 22E47 ; quantum groups ; intertwining differential operators ; conformal invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We first recall a canonical procedure for the construction of the invariant differential operators and equations for arbitrary complex or real noncompact semisimple Lie groups. Then we present the application of this procedure to the case of quantum groups. In detail is given the construction of representations of the quantum algebra U q (sl(n)) labelled by n−1 complex numbers and acting in the spaces of functions of n(n−1)/2 noncommuting variables, which generate a q-deformed SL(4) flag manifold. The conditions for reducibility of these representations and the procedure for the construction of the q-difference intertwining operators are given. Using these results for the case n=4 we propose infinite hierarchies of q-difference equations which are q-conformal invariant. The lowest member of one of these hierarchies are new q-Maxwell equations. We propose also new q-Minkowski spacetime which is part of a q-deformed SU(2,2) flag manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00116517
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  • 2
    Electronic Resource
    Electronic Resource
    Braided bosonization and inhomogeneous quantum groups (1996)
    Springer
    Acta applicandae mathematicae 44 (1996), S. 117-132 
    Details
    ISSN: 1572-9036
    Keywords: 17B37 ; 18D10 ; braided categories ; braided Hopf algebras ; bosonization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider quasitriangular Hopf algebras in braided tensor categories introduced by Majid. It is known that a quasitriangular Hopf algebra H in a braided monoidal category C induces a braiding in a full monoidal subcategory of the category of H-modules in C. Within this subcategory, a braided version of the bosonization theorem with respect to the category C will be proved. An example of braided monoidal categories with quasitriangular structure deviating from the ordinary case of symmetric tensor categories of vector spaces is provided by certain braided supersymmetric tensor categories. Braided inhomogeneous quantum groups like the dilaton free q-Poincaré group are explicit applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00116518
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  • 3
    Electronic Resource
    Electronic Resource
    Askey-Wilson polynomials and the quantum SU(2) group: Survey and applications (1996)
    Springer
    Acta applicandae mathematicae 44 (1996), S. 295-352 
    Details
    ISSN: 1572-9036
    Keywords: 33D45 ; 33D80 ; 17B37 ; 42C05 ; 33C45 ; quantum group ; SU(2) ; Askey-Wilson polynomials ; representation theory ; matrix elements ; dual q-Krawtchouk polynomials ; spherical and associated spherical elements ; continuous q-ultraspherical polynomials ; q-Hahn polynomials ; characters ; Chebyshev polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to Lie algebra like elements of the quantised universal enveloping algebra of sl(2). A full proof of the theorem announced by Noumi and Mimachi [Proc. Japan Acad. Sci. Ser. A 66 (1990), 146–149] describing the generalised matrix elements in terms of the full four-parameter family of Askey-Wilson polynomials is given. Various known and new applications of this interpretation are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047396
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  • 4
    Electronic Resource
    Electronic Resource
    Multiparameter quantum function algebra at roots of 1 (1996)
    Springer
    Mathematische Annalen 306 (1996), S. 759-780 
    Details
    ISSN: 1432-1807
    Keywords: 16W30 ; 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01445276
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  • 5
    Electronic Resource
    Electronic Resource
    q-Ultraspherical polynomials for q a root of unity (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 173-180 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 33D80 ; ultraspherical polynomials ; root of unity ; Darboux transformations ; weight functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Properties of the q-ultraspherical polynomials for q being a primitive root of unity, are derived using a formalism of the so q (3) algebra. The orthogonality condition for these polynomials provides a new class of trigonometric identities representing discrete finite-dimensional analogues of q-beta integrals of Ramanujan.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00416020
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  • 6
    Electronic Resource
    Electronic Resource
    A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions (1996)
    Springer
    Letters in mathematical physics 38 (1996), S. 33-51 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 17B65 ; 81R50 ; quantum deformation ; Virasoro algebra ; bosonic realization ; Macdonald symmetric functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398297
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  • 7
    Electronic Resource
    Electronic Resource
    Quadratic Poisson brackets and the Drinfeld theory for associative algebras (1996)
    Springer
    Letters in mathematical physics 38 (1996), S. 63-75 
    Details
    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81R99 ; Poisson brackets ; associative algebra ; Yang-Baxter equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Letter is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang-Baxter equation are revealed. The Letter also contains a description of Poisson Lie structures on Lie groups whose Lie algebras are adjacent to an associative structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398299
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  • 8
    Electronic Resource
    Electronic Resource
    Eigenvalues of Casimir invariants for type I quantum superalgebras (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 415-425 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30 ; Casimir invariants ; quantum algebras ; Yang-Baxter equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714406
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  • 9
    Electronic Resource
    Electronic Resource
    A candidate for a noncompact quantum group (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 157-167 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 16W30 ; 22D10 ; 46H99 ; star products ; noncompact quantum groups ; Hopf algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A previous letter (Bidegain, F. and Pinczon, G:Lett. Math. Phys. 33 (1995), 231–240) established that the star-product approach of a quantum group introduced by Bonneau et al. can be extended to a connected locally compact semisimple real Lie group. The aim of the present Letter is to give an example of what a noncompact quantum group could be. From half of the discrete series ofSL(2, $$\mathbb{R}$$ ), a new type of quantum group is explicitly constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00714378
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  • 10
    Electronic Resource
    Electronic Resource
    Highest weight representations of quantum current algebras (1996)
    Springer
    Letters in mathematical physics 36 (1996), S. 319-326 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 17B65 ; 81T10 ; Lie algebras ; highest weight representations ; tensor product representations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the highest weight and continuous tensor product representations ofq-deformed Lie algebras through the mappings of a manifold into a locally compact group. As an example the highest weight representation of theq-deformed algebra slq(2,ℂ) is calculated in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00943284
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