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Quantum Algebra papers — page 13

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The Reversed q-Exponential Functional Relation
After obtaining some useful identities, we prove an additional functional relation for q exponentials with reversed order of multiplication, as well as the well known direct one in a completely…
David Fairlie, Ming-Yuan WuApr 17, 1997
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Cartan-Weyl Basis for Yangian Double DY(sl3)
We give a new realization of Y(sl3) via Cartan-Weyl elements. An algebraic description of Yangian Double DY(sl3), explicit comultiplication formulas and universal R-matrix are obtained in these…
Alexandre SolovievApr 13, 1997
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Quantum Hall Effect Wave Functions as Cyclic Representations of Uq(sl(2))
Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra…
O. F. DayiApr 11, 1997
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Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail…
E. Frenkel, N. Reshetikhin, M. A. Semenov-Tian-ShanskyApr 11, 1997
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Lie Bialgebra Structures on Twodimensional Galilei Algebra and their Lie-Poisson Counterparts
All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.
Emil KowalczykApr 10, 1997
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Generalized Rationality and a "Jacobi Identity" for Intertwining Operator Algebras
We prove a generalized rationality property and a new identity that we call the ``Jacobi identity'' for intertwining operator algebras. Most of the main properties of genus-zero conformal…
Yi-Zhi HuangApr 9, 1997
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Quantum groups and representations with highest weight
We consider a special category of Hopf algebras, depending on parameters Σ which possess properties similar to the category of representations of simple Lie group with highest weight λ. We…
Joseph Bernstein, Tanya KhovanovaApr 8, 1997
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Non-standard quantum so(3,2) and its contractions
A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are…
Francisco J. HerranzApr 7, 1997
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SL(2,Z)-Invariant Spaces Spanned by Modular Units
Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E+ of modular…
Wolfgang Eholzer, Nils-Peter SkoruppaApr 3, 1997
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Elliptic quantum groups and Ruijsenaars models
We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups Eτ,η(glN). The corresponding transfer matrices give rise to various integrable difference…
Giovanni Felder, Alexander VarchenkoApr 3, 1997
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Introduction to quantum groups
We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra…
P. Podles, E. MullerApr 2, 1997
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Jones-Wassermann Subfactors for Disconnected Intervals
We show that the Jones-Wassermann subfactors for disconnected intervals, which are constructed from the representations of loop groups of type A, are finite-depth subfactors. The index value and…
Feng XuApr 2, 1997
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Highest weight representations of the quantum algebra Uh(gl∞)
A class of highest weight irreducible representations of the quantum algebra Uh(gl∞) is constructed. Within each module a basis is introduced and the transformation relations of the basis…
T. D. Palev, N. I. StoilovaApr 2, 1997
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The algebra A,η(g) and Infinite Hopf family of algebras
New deformed affine algebras A,η(g) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A,η(sl2) recently proposed by…
Bo-Yu Hou, Liu Zhao, Xiang-Mao DingMar 30, 1997
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Cauchy identities for universal Schubert polynomials
We prove the Cauchy type identities for the universal double Schubert polynomials, introduced recently by W. Fulton. As a corollary, the determinantal formulae for some specializations of the…
Anatol N. KirillovMar 30, 1997
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Polyhedral Realizations of Crystal Bases for Quantized Kac-Moody Algebras
Let B(∞) be the crystal corresponding to the nilpotent part of a quantized Kac-Moody algebra. We suggest a general way to represent B(∞) as the set of integer solutions of a system of…
Toshiki Nakashima, Andrei ZelevinskyMar 28, 1997
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Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group Uq(sl2) is a system of linear difference equations with values in a tensor product of…
Vitaly Tarasov, Alexander VarchenkoMar 27, 1997
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Classical Limit of the Scaled Elliptic Algebra A,η(sl2)
The classical limit of the scaled elliptic algebra A,η(sl2) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of…
S. Khoroshkin, D. Lebedev, S. Pakuliak et al.Mar 27, 1997
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Two types of Poisson pencils and related quantum objects
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in…
D. Gurevich, J. Donin, V. RubstovMar 26, 1997
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Dual quasitriangular structures related to the Temperley-Lieb algebra
We consider nonquasiclassical solutions to the quantum Yang-Baxter equation and the corresponding quantum cogroups (SL(S)) constructed earlier by one of the authors . We give a criterion of the…
P. Akueson, D. GurevichMar 24, 1997
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Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
The classical Yang-Baxter equation (CYBE) is an algebraic equation central in the theory of integrable systems. Its solutions were classified by Belavin and Drinfeld. Quantization of CYBE led to the…
Pavel Etingof, Alexander VarchenkoMar 21, 1997
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Quommutator deformations of spl(N,1)
We analyse the Witten-Woronowicz's type deformations of the Lie superalgebras spl(N,1) and obtain deformations parametrized by N(N-1)/2 independent parameters for N>2 and by three parameters for…
Yves BrihayeMar 21, 1997
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A Natural Basis of States for the Noncommutative Sphere and its Moyal bracket
An infinite dimensional algebra which is a non-decomposable reducible representation of su(2) is given. This algebra is defined with respect to two real parameters. If one of these parameters is…
J. GratusMar 21, 1997
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The boundary of Young graph with Jack edge multiplicities
Consider the lattice of all Young diagrams ordered by inclusion, and denote by Y its Hasse graph. Using the Pieri formula for Jack symmetric polynomials, we endow the edges of the graph Y with formal…
Sergei Kerov, Andrei Okounkov, Grigori OlshanskiMar 21, 1997
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Differential Calculus in Braided Abelian Categories
Braided non-commutative differential geometry is studied. In particular we investigate the theory of (bicovariant) differential calculi in braided abelian categories. Previous results on crossed…
Yuri Bespalov, Bernhard DrabantMar 20, 1997
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