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Quantum Algebra papers — page 3

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Cellular algebras arising from Hecke algebras of type Hn
We study a finite-dimensional quotient of the Hecke algebra of type Hn for general n, using a calculus of diagrams. This provides a basis of monomials in a certain set of generators. Using this,…
R. M. GreenDec 4, 1997
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Generalized Temperley-Lieb algebras and decorated tangles
We give presentations, by means of diagrammatic generators and relations, of the analogues of the Temperley-Lieb algebras associated as Hecke algebra quotients to Coxeter graphs of type B and D.…
R. M. GreenDec 4, 1997
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Dynamical systems related to the Cremmer-Gervais R-matrix
The generalized Cremmer-Gervais R-matrix being a twist of the standard R-matrix of SLq(3), depends on two extra parameters. Properties of this R-matrix are discussed and two dynamical systems, the…
M. Chaichian, P. Kulish, E. V. DamaskinskyDec 4, 1997
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Dual Affine Quantum Groups
Let g be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let h be the dual Lie bialgebra. By dualizing the…
Fabio GavariniDec 3, 1997
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Classification of Low Dimensional Lie Super-Bialgebras
A thorough analysis of Lie super-bialgebra structures on Lie super-algebras osp(1|2) and super-e(2) is presented. Combined technique of computer algebraic computations and a subsequent identification…
Cezary Juszczak, Jan T. SobczykDec 3, 1997
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Commutation relations of vertex operators related with the spin representation of Uq(Dn(1))
We calculate commutation relations of vertex operators for the spin representation of Uq(Dn(1)) by using recursive formulae of R-matrices. In quantum symmetry approach, we obtain the energy…
Yoshiyuki KogaDec 3, 1997
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Perfect Crystals of Uq(G2(1))
The notion of perfect crystals was introduced in "Perfect Crystal and Vertex Models", (Internat. J. Modern Phys. A7(1992)449-484) by S-J. Kang et al. In this paper, we give a series of…
Sigenori YamaneDec 3, 1997
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On Super RS algebra and Drinfeld Realization of Quantum Affine Superalgebras
We describe the realization of the super Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel-Reshetikhin to the supersymmetric…
Mark D. Gould, Yao-Zhong ZhangDec 3, 1997
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Fourier Knots
This paper introduces the concept of a Fourier knot. A Fourier knot is a knot that is represented by a parametrized curve in three dimensional space such that the coordinate functions are finite…
Louis H. KauffmanDec 3, 1997
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A proof of Feigin's conjecture
The paper is devoted to the proof of the following conjecture due to B. Feigin. Let u be the small quantum group a the primitive -th root of unity. Then it is known that the usual…
Sergey ArkhipovDec 2, 1997
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Noncommutative analogues of q-special polynomials and q-integral on a quantum sphere
The q-Legendre polynomials can be treated as some special "functions in the quantum double cosets U(1) SUq(2)/U(1)". They form a family (depending on a parameter q) of…
D. Gurevich, L. VainermanDec 2, 1997
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Cohomology of the Lie algebras of differential operators: lifting formulas
We construct the explicit formula for the (2n+1)-cocycle of the Lie algebra of (pseudo)differential operators on a n-dimensional space. We prove that this formula in fact defines a cocycle for n=1…
Boris ShoikhetDec 1, 1997
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Twist Deformation of the rank one Lie Superalgebra
The Drinfeld twist is applyed to deforme the rank one orthosymplectic Lie superalgebra osp(1|2). The twist element is the same as for the sl(2) Lie algebra due to the embedding of the sl(2)…
E. Celeghini, P. P. KulishDec 1, 1997
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On Irreducibility of Tensor Products of Yangian Modules
We study the tensor product V of any number of "elementary" irreducible modules over the Yangian of the general linear Lie algebra. An elementary module is determined by a skew Young diagram and by…
Maxim Nazarov, Vitaly TarasovNov 30, 1997
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Five Lectures on Soliton Equations
This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez.
Edward FrenkelNov 30, 1997
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Spiders for rank 2 Lie algebras
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and…
Greg KuperbergNov 29, 1997
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On solutions of the KZ and qKZ equations at level zero
We discuss relations between different formulae for solutions of the Knizhnik-Zamolodchikov differential and the quantum Knizhnik-Zamolodchikov difference equations at level 0 and associated with…
A. Nakayashiki, S. Pakuliak, V. TarasovNov 29, 1997
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Yang-Baxter systems, solutions and applications
Two types of Yang-Baxter systems play roles in the theoretical physics -- constant and colour dependent. The constant systems are used mainly for construction of special Hopf algebra while the colour…
L. HlavatyNov 28, 1997
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Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra
We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space…
M. Lagraa, N. TouhamiNov 28, 1997
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FRT Quantization Theory for the Nonsemisimple Cayley-Klein Groups
The quantization theory of the simple Lie groups and algebras was developed by Faddeev-Reshetikhin-Takhtadjan (FRT). In group theory there is a remarkable set of groups, namely the motion groups of…
N. A. Gromov, I. V. Kostyakov, V. V. KuratovNov 26, 1997
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Finite-dimensional irreducible representations of twisted Yangians
We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras…
Alexander MolevNov 25, 1997
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The consistent reduction of the differential calculus on the quantum group GLq(2,C) to the differential calculi on its subgroups and σ-models on the quantum group manifolds SLq(2,R), SLq(2,R)/Uh(1), Cq(2|0) and infinitesimal transformations
Explicit construction of the second order left differential calculi on the quantum group and its subgroups are obtained with the property of the natural reduction: the differential calculus on the…
V. D. GershunNov 24, 1997
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Poincaré Series of Quantum Spaces Associated to Hecke Operators
We study the Poincaré series of the quantum spaces associated to a Hecke operator, i.e., a Yang-Baxter operator satisfying the equation (x+1)(x-q)=0. The Poincaré series of the corresponding matrix…
Phung Ho HaiNov 23, 1997
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A skein theoretic proof of the hook formula for quantum dimension
We give a skein theoretic proof the Reshetikhin hook length formula for quantum dimension for the quantum group Uq(sl(N)).
A. K. AistonNov 20, 1997
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A one-dimensional many-body integrable model from Zn Belavin model with open boundary conditions
We use factorized L operator to construct an integrable model with open boundary conditions. By taking trigonometic limit(τ -1∞) and scaling limit(ω 0), we get a Hamiltonian…
Heng Fan, Bo-Yu Hou, Guang-Liang Li et al.Nov 20, 1997
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