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Quantum Algebra papers — page 47

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Representations of generalized oscillator algebra
The representations of the oscillator algebra introduced by Brzezinski et al. (Phys. Lett. B 311 (1993), 202) are classified.
P. Kosinski, M. Majewski, P. MaslankaJan 12, 1995
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Differential calculus on deformed E(2) group
Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.
S. Giller, C. Gonera, P. Kosinski et al.Jan 12, 1995
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Bicrossproduct Hopf Superalgebras and D=4 κ-deformed Poincaré Supergroup.
The general framework of bicrossproduct Hopf algebras given by Majid is extended to Z2-graded bicrossproduct Hopf superalgebras. As examples of bicrossproduct Hopf superalgebras we provide the…
P. Kosi{ń}ski, J. Lukierski, P. Ma{ś}lanka et al.Jan 12, 1995
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Covariant Differential and Integral Calculi for Lattice (l,q)-deformed Fields
Using the Hecke R-matrix, we give a definition of the lattice (l,q)-deformed n-component boson and Grassmann fields. Here l is a deformation parameter for the commutation relations of…
A. Bugrij, V. Rubtsov, V. ShaduraJan 9, 1995
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Quantization of Poisson pencils and generalized Lie algebras
We describe two types of Poisson pencils generated by a linear bracket and a quadratic one arising from a classical R-matrix. A quantization scheme is discussed for each. The quantum algebras are…
D. Gurevich, V. RubtsovJan 9, 1995
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Quantum Groups,Deformed Oscillators and their Interrelations
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: GLq(2), slq(2), q-oscillator algebra $…
E. V. Damaskinsky, P. P. KulishJan 6, 1995
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q-Bosonization of the quantum group GLq(2) based on the Gauss decomposition
The new method of q-bosonization for quantum groups based on the Gauss decomposition of a transfer matrix of generators is suggested. The simplest example of the quantum group GLq(2) is considered…
E. V. Damaskinsky, M. A. SokolovJan 6, 1995
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Invariants for 1-dimensional cohomology classes arising from TQFT
Let (V,Z) be a Topological Quantum Field Theory over a field f defined on a cobordism category whose morphisms are oriented n+1-manifolds perhaps with extra structure. Let (M,χ) be a closed…
Patrick GilmerJan 4, 1995
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Quantum affine algebras and affine Hecke algebras
We describe a connection between finite--dimensional representations of quantum affine algebras and affine Hecke algebras.
Vyjayanthi Chari, Andrew PressleyJan 3, 1995
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A Littlewood-Richardson filtration at roots of 1 for multiparameter deformations of skew Schur modules.
Let R be a commutative ring, q a unit of R and P a multiplicatively antisymmetric matrix with coefficients which are integers powers of q. Denote by SE(q,P) the multiparameter quantum matrix…
G. Boffi, M. VaragnoloJan 2, 1995
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On the deformation of abelian integrals
We consider the deformation of abelian integrals which arose from the study of SG form factors. Besides the known properties they are shown to satisfy Riemann bilinear identity. The deformation of…
F. A. SmirnovJan 2, 1995
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Localization of u-modules. II. Configuration spaces and quantum groups
This paper is a sequel to "Localization of u-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category C associated with a quantum group…
M. Finkelberg, V. SchechtmanJan 1, 1995
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Macdonald's Evaluation Conjectures and Difference Fourier Transform
In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and…
Ivan CherednikDec 30, 1994
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Vertex--IRF correspondence and factorized L-operators for an elliptic R-operator
As for an elliptic R-operator which satisfies the Yang--Baxter equation, the incoming and outgoing intertwining vectors are constructed, and the vertex--IRF correspondence for the elliptic…
Youichi ShibukawaDec 28, 1994
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Modular forms associated with the Monster module
We investigate the relation between the generating functions of the highest weight vectors of the Monster module and the McKay-Thompson series.
Koichiro Harada, Mong Lung LangDec 28, 1994
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The McKay-Thompson series associated with the irreducible characters of the Monster
Let V = h = 0∞ Vh be the graded monster module of the monster simple group M and let χk be an irreducible representation of M. The generating function…
Koichiro Harada, Mong Lung LangDec 28, 1994
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Highest Weight Representations of Quantum Current Algebras
We study the highest weight and continuous tensor product representations of q-deformed Lie algebras through the mappings of a manifold into a locally compact group. As an example the highest weight…
Sergio Albeverio, Shao-Ming FeiDec 22, 1994
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Differential Calculus on the Quantum Sphere and Deformed Self-Duality Equation
We discuss the left-covariant 3-dimensional differential calculus on the quantum sphere SUq (2)/U(1) . The SUq (2)-spinor harmonics are treated as coordinates of the quantum sphere. We consider…
B. M. ZupnikDec 22, 1994
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Classification of the GL(3) Quantum Matrix Groups
We define quantum matrix groups GL(3) by their coaction on appropriate quantum planes and the requirement that the Poincare series coincides with the classical one. It is shown that this implies the…
Holger Ewen, Oleg OgievetskyDec 21, 1994
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Projective Systems of Imprimitivity
We apply Mackey procedure of classifying projective systems of imprimitivity to a thorough study of the projective unitary irreducible representations of the Galilei group in 1+3 and 1+2 dimensions.
Dan Radu GrigoreDec 20, 1994
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Central elements for quantum affine algebras and affine Macdonald's operators
We describe a generalization of Drinfeld's description of the center of a quantum group to the case of quantum affine algebras. We use the obtained central elements to construct the affine…
Pavel EtingofDec 20, 1994
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Classical Spinor Structures on Quantum Spaces
A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular,…
Mico DurdevicDec 19, 1994
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Geometry of Quantum Principal Bundles II-Extended Version
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential…
Mico DurdevicDec 19, 1994
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On Differential Structures on Quantum Principal Bundles
A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential)…
Mico DurdevicDec 19, 1994
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On Braided Quantum Groups
A braided generalization of the concept of Hopf algebra (quantum group) is presented. The generalization overcomes an inherent geometrical inhomogeneity of quantum groups, in the sense of allowing…
Mico DurdevicDec 19, 1994
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