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Quantum Algebra papers — page 26

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On the Completeness of Some Subsystems of q-deformed Coherent States
The von Neumann type subsystems of q-deformed coherent states are considered. The completeness of such subsystems is proved.
A. M. PerelomovJul 5, 1996
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Linear Connections on Graphs
In recent years, discrete spaces such as graphs attract much attention as models for physical spacetime or as models for testing the spirit of non-commutative geometry. In this work, we construct the…
Sunggoo Cho, Kwang Sung ParkJul 4, 1996
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Multivariable q-Racah polynomials
The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measure becomes discrete…
Jan F. van Diejen, Jasper V. StokmanJul 1, 1996
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Quantum groups and q-lattices in phase space
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group…
J. WessJul 1, 1996
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Vassiliev and Quantum Invariants of Braids
We prove that braid invariants coming from quantum gl(N) separate braids, by recalling that these invariants (properly decomposed) are all Vassiliev invariants, showing that all Vassiliev invariants…
Dror Bar-NatanJul 1, 1996
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Character States and Generator Matrix Elements for Sp(4) ⊃ SU(2) × U(1): Generic Representation
A new set of polynomial states (to be called character states) are derived for Sp(4) reduced to its SU(2) × U(1) subgroup, and the relevant generator matrix elements are evaluated for…
N. Hambli, J. Michelson, R. T. SharpJun 30, 1996
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Polynomial Invariants are Polynomial
We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type m is evaluated on a knot projection having n crossings, the result is bounded by a constant times nm. Thus the…
Dror Bar-NatanJun 30, 1996
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Two-parameter quantum groups and quantum planes
Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not…
Sunggoo Cho, Sang-jun Kang, Chung-hum Kim et al.Jun 29, 1996
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Geometric interpretation of the Poisson structure in affine Toda field theories
We express the Poisson brackets of local fields of the affine Toda field theories in terms of the Drinfeld-Sokolov dressing operator. For this, we introduce a larger space of fields, containing…
Benjamin Enriquez, Edward FrenkelJun 27, 1996
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On Associators and the Grothendieck-Teichmuller Group I
We present a formalism within which the relationship (discovered by Drinfel'd) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group…
Dror Bar-NatanJun 26, 1996
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The bicovariant differential calculus on the kappa-Poincare and kappa-Weyl groups
The bicovariant differential calculus on fourdimensional kappa-Poincare group and corresponding Lie-algebra like structure for any metric tensor are described. The bicovariant differential calculus…
Karol PrzanowskiJun 26, 1996
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Generalization and Exact Deformations of Quantum Groups
A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position.…
Christian FronsdalJun 25, 1996
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Braided modules and reflection equations
We introduce a representation theory of q-Lie algebras defined earlier in DG1, DG2, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects…
D. GurevichJun 25, 1996
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Bispectral Darboux Transformations: The Generalized Airy Case
This paper considers Darboux transformations of a bispectral operator which preserve its bispectrality. A sufficient condition for this to occur is given, and applied to the case of generalized Airy…
Alex Kasman, Mitchell RothsteinJun 24, 1996
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L'algebre de Hopf bitensorielle
Nous construisons pour tout corps k de caracteristique zero un foncteur de la categorie des k-espaces vectoriels dans la categorie des k-algebres de Hopf pointees, qui a tout espace vectoriel V…
Dominique ManchonJun 24, 1996
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Lie Algebras and the Four Color Theorem
We present a ``reasonable'' statement about Lie algebras that is equivalent to the Four Color Theorem. The notions appearing in the statement also appear in the theory of finite-type…
Dror Bar-NatanJun 23, 1996
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Irreducible Representations of Jordanian Quantum Algebra Uh(sl(2)) Via a Nonlinear Map
The generators of the Jordanian quantum algebra Uh(sl(2)) are expressed as nonlinear invertible functions of the classical sl(2) generators. This permits immediate explicit construction…
B. Abdesselam, A. Chakrabarti, R. ChakrabartiJun 19, 1996
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A cellular braid action and the Yang - Baxter equation
Using a theorem of Schechtman - Varchenko on integral expressions for solutions of Knizhnik - Zamolodchikov equations we prove that the solutions of the Yang - Baxter equation associated to complex…
Mirko LueddeJun 19, 1996
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On the existence of deformed Lie-Poisson structures for quantized groups
The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structure. It serves as a natural analogue of classical…
V. D. Lyakhovsky, A. M. MirolubovJun 17, 1996
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Link invariants from N-state vertex models: an alternative construction independent of statistical models
We reproduce the hierarchy of link invariants associated to the series of N-state vertex models with a method different from the original construction due to Akutsu, Deguchi and Wadati. The…
M. J. Rodriguez-PlazaJun 13, 1996
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Noncommutative geometry and its relation to stochastic calculus and symplectic mechanics
In the context of a noncommutative differential calculus on the algebra of real valued functions of an n-dimensional manifold M, a commutative and associative product of 1-forms is naturally…
A. Dimakis, C. TzanakisJun 13, 1996
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From quantum affine groups to the exact dynamical correlation function of the Heisenberg model
The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. We use them to derive an…
A. H. Bougourzi, M. Couture, M. KacirJun 11, 1996
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Geometric Construction of Crystal Bases
We realize the crystal associated to the quantized enveloping algebras with a symmetric generalized Cartan matrix as a set of Lagrangian subvarieties of the cotangent bundle of the quiver variety. As…
Masaki Kashiwara, Yoshihisa SaitoJun 8, 1996
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Factorial supersymmetric Schur functions and super Capelli identities
A factorial analogue of the supersymmetric Schur functions is introduced. It is shown that factorial versions of the Jacobi--Trudi and Sergeev--Pragacz formulae hold. The results are applied to…
Alexander MolevJun 7, 1996
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Semiquantum Geometry
In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures, which we call Poisson fibred algebras,…
Nicolai Reshetikhin, Alexander A. Voronov, Alan WeinsteinJun 5, 1996
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