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Quantum Algebra papers — page 9

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The q-Deformed Oscillator Representations and Their Coherent States of the su(1,1) Algebra
We present various oscillator representations of the q-deformed su(1,1) algebra such as the Holstein-Primakoff, the Dyson, the Fock-Bargmann, the anyonic, and the parabose oscillator representations…
Phillial Oh, Chaiho RimJul 25, 1997
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Double quantization on the coadjoint representation of sl(n)
For =sl(n) we construct a two parametric Uh()-invariant family of algebras, (S)t,h, which defines a quantization of the function algebra S on the coadjoint representation and in…
J. DoninJul 24, 1997
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On the Hopf algebra structure of perturbative quantum field theories
We show that the process of renormalization encapsules a Hopf algebra structure in a natural manner. This sheds light on the recently proposed connection between knots and renormalization theory.
Dirk KreimerJul 23, 1997
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Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation
In this paper we construct homogeneous star products of Weyl type on every cotangent bundle T*Q by means of the Fedosov procedure using a symplectic torsion-free connection on T*Q homogeneous…
Martin Bordemann, Nikolai Neumaier, Stefan WaldmannJul 23, 1997
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A Littlewood-Richardson Rule for factorial Schur functions
We give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial Schur functions. It is a special case of a more general rule which also gives the…
Alexander I. Molev, Bruce E. SaganJul 23, 1997
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On set-theoretical solutions of the quantum Yang-Baxter equation
Recently V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions of the quantum Yang-Baxter equation, i.e.…
Pavel Etingof, Travis Schedler, Alexandre SolovievJul 22, 1997
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Explicit Decompositions of Weyl Reflections in Affine Lie Algebras
In this paper explicit decompositions are provided of the Weyl reflections in affine Lie algebras, in terms of fundamental Weyl reflections.
J. RasmussenJul 21, 1997
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Bicrossproduct structure of the null-plane quantum Poincare algebra
A nonlinear change of basis allows to show that the non-standard quantum deformation of the (3+1) Poincare algebra has a bicrossproduct structure. Quantum universal R-matrix, Pauli-Lubanski and mass…
Oscar Arratia, Francisco J. Herranz, Mariano A. del OlmoJul 21, 1997
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Some comments on q-deformed oscillators and q-deformed su(2) algebras
The various relations between q-deformed oscillators algebras and the q-deformed su(2) algebras are discussed. In particular, we exhibit the similarity of the q-deformed su(2) algebra…
L. C. Kwek, C. H. OhJul 18, 1997
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Deformed harmonic oscillators : coherent states and Bargmann representations
Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by…
M. Irac-Astaud, G. RideauJul 17, 1997
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Algebraic geometry of Hopf-Galois extensions
We continue the study of Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We concentrate on the geometrical side on the subject. We understand how to localize…
Dmitriy RumyninJul 16, 1997
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Hopf-Galois extensions with central invariants
We study Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We collect general facts about them and discuss some examples arising in the study of restricted Lie…
Dmitriy RumyninJul 16, 1997
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Bargmann representations for deformed harmonic oscillators
Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by…
M. Irac-Astaud, G. RideauJul 15, 1997
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Dynamical r-matrices for Hitchin's systems on Schottky curves
We express Hitchin's systems on curves in Schottky parametrization, and construct dynamical r-matrices attached to them.
B. EnriquezJul 15, 1997
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Nonabelian Integrable Systems, Quasideterminants, and Marchenko Lemma
We find explicit (multisoliton) solutions for nonabelian integrable systems such as periodic Toda field equations, Langmuir equations, and Schrodinger equations for functions with values in any…
Pavel Etingof, Israel Gelfand, Vladimir RetakhJul 14, 1997
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Automorphisms of the Weyl algebra and bispectral operators
In our previous paper q-alg/9605011 we proposed several algebraic methods for constructing new solutions to the bispectral problem. In the present note the corresponding eigenfunctions are explicitly…
B. Bakalov, E. Horozov, M. YakimovJul 14, 1997
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Connes' distance function on one-dimensional lattices
We show that there is an operator with a simple geometric significance which yields the ordinary geometry of a linear equidistant lattice via Connes' distance function.
Aristophanes Dimakis, Folkert Müller-HoissenJul 14, 1997
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On braided Poisson and quantum inhomogeneous groups
The well known incompatibility between inhomogeneous quantum groups and the standard q-deformation is shown to disappear (at least in certain cases) when admitting the quantum group to be braided.…
S. ZakrzewskiJul 13, 1997
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Crystals for Demazure Modules of Classical Affine Lie Algebras
We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types A(1)n,B(1)n,C(1)n,D(1)n, A(2)2n-1,A(2)2n, and D(2)n+1. We find a…
A. Kuniba, K. C. Misra, M. Okado et al.Jul 11, 1997
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Coinvariants for Yangian doubles and quantum KZ equations
We present a quantum version of the construction of the KZ system of equations as a flat connection on the spaces of coinvariants of representations of tensor products of Kac-Moody algebras. We…
B. Enriquez, G. FelderJul 10, 1997
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q-Uncertainty Relations
As one would anticipate from the realization of the q-commutators by difference operators, the states of maximum localization are smeared delta functions depending on q.
Robert J. FinkelsteinJul 10, 1997
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The symplectic structure of the spin Calogero model
We compute the symplectic structure of the spin Calogero model in terms of algebro-geometric data on the associated spectral curve.
O. Babelon, M. TalonJul 10, 1997
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Knot Invariants from a Kohno-Kontsevich Integral for Braids
An invariant of knots is constructed from an integral for geometric braids due to Kohno and Kontsevich. It takes values in a quotient by a certain ideal of the algebra generated by chord diagrams…
Roger PickenJul 10, 1997
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The prime spectrum of a quantum Bruhat cell translate
The prime spectra of two families of algebras, Sw and Sw, w∈ W, indexed by the Weyl group W of a semisimple finitely dimensional are studied. The algebras Sw have been…
Maria GorelikJul 8, 1997
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Framed vertex operator algebras, codes and the moonshine module
For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1/2, two codes are introduced and studied. It is proved that such vertex…
C. Dong, R. L. Griess, G. HoehnJul 7, 1997
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