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  • Mathematics  (14)
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  • 1
    Electronic Resource
    Electronic Resource
    Quantum groups and diagonalization of the braid generator (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 183-196 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V ⊗ V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00402893
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  • 2
    Electronic Resource
    Electronic Resource
    Two variable link polynomials from quantum supergroups (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 187-198 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract New two variable link polynomials are constructed corresponding to a one-parameter family of representations of the quantum supergroup U q [gl(2 | 1)]. Their connection with the Kauffman polynomials is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420752
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  • 3
    Electronic Resource
    Electronic Resource
    Baxterization of ther-matrix for the adjoint representation of U q [D(2, 1;α)] (1993)
    Springer
    Letters in mathematical physics 27 (1993), S. 51-58 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Baxterization procedure is applied to the Braid group representation arising from the adjoint representation of the quantum supergroup U q [D(2, 1;α)]. This yields a two-parameter family of solutions to the (parameter dependent) Yang-Baxter equation of interest in supersymmetric lattice models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00739589
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  • 4
    Electronic Resource
    Electronic Resource
    On universalR-matrix for quantized nontwisted rank 3 affine KM algebras (1993)
    Springer
    Letters in mathematical physics 29 (1993), S. 19-31 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Explicit formulas of the universalR-matrix are given for all quantized nontwisted rank 3 affine KM algebras U q (A 2 (1) ), U q (C 2 (1) ) and U q (G 2 (1) ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00760855
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  • 5
    Electronic Resource
    Electronic Resource
    Algebraic deformation program on minimal nilpotent orbit (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 241-250 
    Details
    ISSN: 1573-0530
    Keywords: 17B35 ; 17B37 ; 22E46
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00805856
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  • 6
    Electronic Resource
    Electronic Resource
    Quantized affine Lie algebras and diagonalization of braid generators (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 267-277 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751063
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  • 7
    Electronic Resource
    Electronic Resource
    Casimir invariants for quantized affine Lie algebras (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 77-83 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00751173
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  • 8
    Electronic Resource
    Electronic Resource
    Quantum affine algebras and universalR-matrix with spectral parameter (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 101-110 
    Details
    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750144
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  • 9
    Electronic Resource
    Electronic Resource
    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
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750149
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  • 10
    Electronic Resource
    Electronic Resource
    On a possible algebra morphism of U q [osp(1/2n)] onto the deformed oscillator algebra W q (n) (1993)
    Springer
    Letters in mathematical physics 28 (1993), S. 187-193 
    Details
    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We formulate a conjecture stating that the algebra ofn pairs of deformed Bose creation and annihilation operators is a factor algebra of U q [osp(1/2n)], considered as a Hopf algebra, and prove it for then = 2 case. To this end, we show that for any value ofq, U q [osp(1/4)] can be viewed as a superalgebra freely generated by two pairsB 1 ± ,B 2 ± of deformed para-Bose operators. We write down all Hopf algebra relations, an analogue of the Cartan-Weyl basis, the ‘commutation’ relations between the generators and a basis in U q [osp(1/2n)] entirely in terms ofB 1 ± ,B 2 ± .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00745150
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