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Quantum Algebra papers — page 11

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Bosonization of quantum affine groups and its application to the higher spin Heisenberg model
In this paper, we present a detailed analysis of the diagonalization of the higher spin Heisenberg model using its quantum affine symmetry Uq(sl(2)). In particular, we describe the…
A. H. BougourziJun 14, 1997
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A Jordanian quantum two-photon/Schrodinger algebra
A non-standard quantum deformation of the two-photon algebra h6 is constructed, and its quantum universal R-matrix is given. Representations of this new quantum algebra are studied on the Fock…
Angel Ballesteros, Francisco J. Herranz, Preeti ParasharJun 13, 1997
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New Wq,p(sl(2)) algebras from the elliptic algebra Aq,p( sl(2)c)
We construct operators t(z) in the elliptic algebra introduced by Foda et al. Aq,p( sl(2)c). They close an exchange algebra when pm=qc+2 for m integer. In addition they commute…
J. Avan, L. Frappat, M. Rossi et al.Jun 13, 1997
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Inverse Harish-Chandra Transform and Difference Operators
We apply a new technique based on double affine Hecke algebras to the Harish-Chandra theory of spherical zonal functions. The formulas for the Fourier transforms of the multiplications by the…
Ivan CherednikJun 12, 1997
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An analogue of the Hom functor and a generalized nuclear democracy theorem
We give an analogue of the Hom functor and prove a generalized form of the nuclear democracy theorem of Tsuchiya and Kanie by using a notion of tensor product for two modules for a vertex operator…
Haisheng LiJun 12, 1997
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The decomposition of level-1 irreducible highest weight modules with respect to the level-0 actions of the quantum affine algebra U'q(sln)
We decompose the level-1 irreducible highest weight modules of the quantum affine algebra Uq(sln) with respect to the level-0 U'q (sln)--action defined in q-alg/9702024. The…
Kouichi TakemuraJun 12, 1997
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q-Deformation of the Krichever-Novikov Algebra
The recent focus on deformations of algebras called quantum algebras can be attributed to the fact that they appear to be the basic algebraic structures underlying an amazingly diverse set of…
C. H. Oh, K. SinghJun 11, 1997
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Vertex algebras
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories…
Richard E. BorcherdsJun 10, 1997
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Quasitriangular structures on cocommutative Hopf algebras
The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional…
A. A. DavydovJun 9, 1997
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Multivariable Al-Salam & Carlitz polynomials associated with the type A q-Dunkl kernel
The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving…
T. H. Baker, P. J. ForresterJun 5, 1997
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The Aarhus integral of rational homology 3-spheres I: A highly non trivial flat connection on S3
Path integrals don't really exist, but it is very useful to dream that they do exist, and figure out the consequences. Apart from describing much of the physical world as we now know it, these…
Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky et al.Jun 4, 1997
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On Vassiliev Invariants not Coming from Semisimple Lie Algebras
We prove a refinement of Vogel's statement that the Vassiliev invariants of knots coming from semisimple Lie algebras do not generate all Vassiliev invariants. This refinement takes into account…
Jens LieberumJun 4, 1997
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On the affine Temperley-Lieb algebras
We describe the cell structure of the affine Temperley-Lieb algebra with respect to a monomial basis. We construct a diagram calculus for this algebra.
C. K. Fan, R. M. GreenJun 3, 1997
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Coloured quantum universal enveloping algebras
We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter…
C. QuesneJun 2, 1997
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A note on the eight tetrahedron equations
In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that…
Jarmo Hietarinta, Frank NijhoffJun 2, 1997
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Duality for the Jordanian Matrix Quantum Group GLg,h(2)
We find the Hopf algebra Ug,h dual to the Jordanian matrix quantum group GLg,h(2). As an algebra it depends only on the sum of the two parameters and is split in two subalgebras:…
B. L. Aneva, V. K. Dobrev, S. G. MihovMay 29, 1997
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Poincaré series of the Weyl group of elliptic Lie algebras A(1,1)1 and A(1,1) 1
In this note, we calculate the Poincaré series of elliptic Weyl groups of type A(1,1)1 and A(1,1) 1 and show that they have a simple expression.
Minoru WakimotoMay 29, 1997
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Jordanian Uh,sgl(2) and its coloured realization
A two-parametric non-standard (Jordanian) deformation of the Lie algebra gl(2) is constructed, and then, exploited to obtain a new, triangular R-matrix solution of the coloured Yang-Baxter…
Preeti ParasharMay 28, 1997
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Quasideterminants, I
Our experience shows that dealing with noncommutative objects one should not imitate the classical commutative mathematics, but follow "the way it is" starting with basics. In this paper we…
I. Gelfand, V. RetakhMay 28, 1997
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Classification of the quantum deformation of the superalgebra GL(1|1)
We present a classification of the possible quantum deformations of the supergroup GL(1|1) and its Lie superalgebra gl(1|1). In each case, the (super)commutation relations and the Hopf structures…
L. Frappat, V. Hussin, G. RideauMay 27, 1997
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Universal Enveloping Algebra and Differential Calculi on Orthogonal q-groups
We review the construction of the multiparametric quantum group ISOq,r(N) as a projection from SOq,r(N+2) and show that it is a bicovariant bimodule over SOq,r(N). The universal…
Paolo Aschieri, Leonardo CastellaniMay 27, 1997
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Coloured Hopf algebras
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined…
C. QuesneMay 27, 1997
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Quantization of Teichmüller spaces and the quantum dilogarithm
The Teichmüller space of punctured surfaces with the Weil-Petersson symplectic structure and the action of the mapping class group is realized as the Hamiltonian reduction of a finite dimensional…
R. M. KashaevMay 27, 1997
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Quantum Group Duality and the Cuntz Algebra
The Cuntz algebra carries in a natural way the structure of a module algebra over the quantized universal enveloping algebra Uq(g), and the structure of a co-module algebra over the quantum group…
A. L. Carey, A. Paolucci, R. B. ZhangMay 27, 1997
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Coloured Hopf algebras
Quite recently, a ``coloured'' extension of the Yang-Baxter equation has appeared in the literature and various solutions of it have been proposed. In the present contribution, we introduce a…
C. QuesneMay 27, 1997
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