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Quantum Algebra papers — page 4

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Screening Currents in Affine Current Algebra
In this paper screening currents of the second kind are considered. They are constructed in any affine current algebra for directions corresponding to simple roots with multiplicity one in a…
J. RasmussenNov 19, 1997
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Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications
This paper is part II of a series of papers on the deformation quantization on the cotangent bundle of an arbitrary manifold Q. For certain homogeneous star products of Weyl ordered type (which we…
Martin Bordemann, Nikolai Neumaier, Stefan WaldmannNov 19, 1997
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Adams operators and knot decorations
We use an explicit isomorphism from the representation ring of the quantum group Uq(sl(N)) to the Homfly skein of the annulus, to determine an element of the skein which is the image of the mth…
A. K. AistonNov 19, 1997
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A spin network generalization of the Jones Polynomial and Vassiliev invariants
We apply the ideas of Alvarez and Labastida to the invariant of spin networks defined by Witten and Martin based on Chern-Simons theory. We show that it is possible to define ambient invariants of…
R. Gambini, J. Griego, J. PullinNov 18, 1997
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Duals of coloured quantum universal enveloping algebras and coloured universal T-matrices
We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras Hc that we recently introduced. We show that if the standard Hopf (super)algebras $…
C. QuesneNov 14, 1997
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Coloured Hopf algebras and their duals
Coloured Hopf algebras, related to the coloured Yang-Baxter equation, are reviewed, as well as their duals. The special case of coloured quantum universal enveloping algebras provides a coloured…
C. QuesneNov 14, 1997
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The nondynamical r-matrix structure for the elliptic An-1 Calogero-Moser model
In this paper, we construct a new Lax operator for the elliptic An-1 Calogero-Moser model with general n(2≤ n) from the classical dynamical twisting,in which the corresponding r-matrix is…
Bo-yu Hou, Wen-li YangNov 14, 1997
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Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels
The spectral decomposition of the path space of the vertex model associated to the level l representation of the quantized affine algebra Uq(sln) is studied. The spectrum and its…
Anatol N. Kirillov, Atsuo Kuniba, Tomoki NakanishiNov 13, 1997
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A Factorization of the Conway Polynomial
A string link S can be closed in a canonical way to produce an ordinary closed link L. We also consider a twisted closing which produces a knot K. We give a formula for the Conway polynomial of L as…
Jerome LevineNov 8, 1997
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Rank one lattice type vertex operator algebras and their automorphism groups
Let L be a positive definite even lattice of rank one and VL+ be the fixed points of the lattice VOA VL associated to L under an automorphism of VL lifting the -1$ isometry of L. A set of…
Chongying Dong, Robert L. GriessNov 7, 1997
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Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials
We examine two isomorphisms between affine Hecke algebras of type A associated with parameters q-1, t-1 and q, t. One of them maps the non-symmetric Macdonald polynomials…
T. H. Baker, P. J. ForresterNov 5, 1997
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Universal R-matrix for null-plane quantized Poincaré algebra
The universal R--matrix for a quantized Poincaré algebra P(3+1) introduced by Ballesteros et al is evaluated. The solution is obtained as a specific case of a formulated…
Andrei MudrovNov 3, 1997
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Biorthogonal polynomials associated with reflection groups and a formula of Macdonald
Dunkl operators are differential-difference operators on RN which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat semigroups, Hermite…
Margit Rösler, Michael VoitNov 3, 1997
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Discretizations of the Schrödinger equation with quantum algebra symmetry
Two quantum Hopf structures for the Schrödinger algebra as well as their corresponding differential-difference realizations are presented. For each case a (space or time) discretization of the…
A. Ballesteros, F. J. Herranz, P. ParasharNov 3, 1997
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Vector Coherent State Realization of Representations of the Affine Lie Algebra sl(2)
The method of vector coherent states is generalized to study representations of the affine Lie algebra sl(2). A large class of highest weight irreps is explicitly constructed, which contains…
R. B. ZhangNov 3, 1997
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On algebraic equations satisfied by hypergeometric solutions of the qKZ equation
We consider the sl(2) quantized Knizhnik-Zamolodchikov equation (qKZ), defined in terms of rational R-matrices. The properties of the equation change when the step of the equation takes a resonance…
E. Mukhin, A. VarchenkoNov 2, 1997
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Quantization of the space of conformal blocks
We consider the discrete Knizhnik-Zamolodchikov connection (qKZ) associated to gl(N), defined in terms of rational R-matrices. We prove that under certain resonance conditions, the qKZ connection…
E. Mukhin, A. VarchenkoOct 31, 1997
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3-State Potts model and automorphism of vertex operator algebra of order 3
We define an automorphism of VOA of order 3 by using a sub VOA isomorphic to a direct sum of 3-state Potts models L(,0) and an its module L(,3). This automorphism is a 3A element of the…
Masahiko MiyamotoOct 31, 1997
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Duality in infinite dimensional Fock representations
We construct and study in detail various dual pairs acting on some Fock representations between a finite dimensional Lie group and a completed infinite rank affine algebra associated to an infinite…
Weiqiang WangOct 28, 1997
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Differential Calculus on Fuzzy Sphere and Scalar Field
We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the…
Ursula Carow-Watamura, Satoshi WatamuraOct 28, 1997
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dN=0
We study the generalized homology associated with a nilpotent endomorphism d satisfying dN=0. For simplicial modules we construct such nilpotent endomorphisms and we prove a general result…
Michel Dubois-VioletteOct 28, 1997
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Boundary solutions of the quantum Yang-Baxter equation and solutions in three dimensions
Boundary solutions to the quantum Yang-Baxter (qYB) equation are defined to be those in the boundary of (but not in) the variety of solutions to the ``modified'' qYB equation, the latter…
Murray Gerstenhaber, Anthony GiaquintoOct 27, 1997
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Cartan-Weyl basis for Quantum Affine Superalgebra Uq(osp(1|2))
Cartan-Weyl basis for the quantum affine superalgebra Uq(osp(1|2)) is constructed in an explicit form.
Jerzy Lukierski, Valeryi N. TolstoyOct 24, 1997
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Lie Bialgebra Structures for Centrally Extended Two- Dimensional Galilei Algebra and their Lie-Poisson Counterparts
All bialgebra structures for centrally extended Galilei algebra are classified. The corresponding Lie-Poisson structures on centrally extended Galilei group are found.
Anna OpanowiczOct 23, 1997
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Deformations of the classical W-algebras associated to Dn, E6 and G2
We give explicit formulas for the generators of q-deformed W-algebras associated to Lie algebras Dn, E6 and G2, and compute the Poisson brackets between the generators.
Alexander KoganOct 23, 1997
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