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Quantum Algebra papers — page 7

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The Cylinder braiding of the quantum Weyl group of sl2
Is is shown that the quantum Weyl group of sl2 contains an element that is a cylinder twist, i.e. it gives rise to representations of the braid group of Coxeter type B.
Reinhard H"aring-OldenburgSep 12, 1997
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Clifford Hopf-gebra and Bi-universal Hopf-gebra
We consider a pair of independent scalar products, one scalar product on vectors, and another independent scalar product on dual space of co-vectors. The Clifford co-product of multivectors is…
Zbigniew OziewiczSep 11, 1997
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The reduced Birman-Wenzl algebra of Coxeter type B
We introduce a reduced form of a Birman-Murakami-Wenzl Algebra associated to the braid group of Coxeter type B and investigate its semisimplicity, Bratteli diagram and Markov trace. Applications in…
R. Haering-OldenburgSep 11, 1997
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Quantum currents realization of the elliptic quantum groups Eτ,η(sl2)
We review the construction by G. Felder and the author of the realization of the elliptic quantum groups of sl(2)-type by quantum currents.
B. EnriquezSep 11, 1997
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An Elliptic Algebra Uq,p(sl2) and the Fusion RSOS Model
We introduce an elliptic algebra Uq,p(sl2) with p=q2r (r∈ >0) and present its free boson representation at generic level k. We show that this algebra governs a structure of…
Hitoshi KonnoSep 9, 1997
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Noncommutativity and Discrete Physics
The purpose of this paper is to present an introduction to a point of view for discrete foundations of physics. In taking a discrete stance, we find that the initial expression of physical theory…
Louis H. KauffmanSep 7, 1997
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Asymptotics of Jack polynomials as the number of variables goes to infinity
In this paper we study the asymptotic behavior of the Jack rational functions as the number of variables grows to infinity. Our results generalize the results of A. Vershik and S. Kerov obtained in…
Andrei Okounkov, Grigori OlshanskiSep 5, 1997
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Domino tableaux, Schutzenberger involution, and the symmetric group action
We define an action of the symmetric group on the set of domino tableaux, and prove that the number of domino tableaux of a given weight does not depend on the permutation of components of the last.…
Arkady Berenstein, Anatol N. KirillovSep 4, 1997
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Quantum two-photon algebra from non-standard Uz(sl(2,R)) and a discrete time Schrödinger equation
The non-standard quantum deformation of the (trivially) extended sl(2,R) algebra is used to construct a new quantum deformation of the two-photon algebra h6 and its associated quantum universal…
Angel Ballesteros, Francisco J. Herranz, Preeti ParasharSep 3, 1997
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The idea of locality
This is a review of recent results on conformal (super)algebras. It may be viewed as an amplification of my Wigner medal acceptance speech (given in July 1996 in Goslar, Germany) reproduced in the…
Victor G. KacSep 2, 1997
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Γ-Conformal Algebras
Γ-conformal algebra is an axiomatic description of the operator product expansion of chiral fields with simple poles at finitely many points. We classify these algebras and their representations in…
Maria Golenishcheva-Kutuzova, Victor KacSep 1, 1997
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A q-deformation of the parastatistics and an alternative to the Chevalley description of Uq[osp(2n+1/2m)]
The paper contains essentially two new results. Physically, a deformation of the parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to the Chevalley…
T. D. PalevSep 1, 1997
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Bilinear Identity for q-Hypergeometric Integrals
We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de…
Vitaly TarasovSep 1, 1997
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The Jordanian deformation of su(2) and Clebsch-Gordan coefficients
Representation theory for the Jordanian quantum algebra U=Uh(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the…
J. Van der JeugtSep 1, 1997
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Highest weight irreducible representations of the quantum algebra Uh(A∞)
A class of highest weight irreducible representations of the algebra Uh(A∞), the quantum analogue of the completion and central extension A∞ of the Lie algebra gl∞, is…
T. D. Palev, N. I. StoilovaSep 1, 1997
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On the nonhamiltonian interaction of two rotators. II. Unraveling the algebraic structure
This note being is devoted to the unraveling of the algebraic structure, which governs the quadratic nonhamiltonian interaction of two rotators described in the first part. It should be considered in…
Denis V. JurievSep 1, 1997
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Noncommutative Geometry of the h-deformed Quantum Plane
The h-deformed quantum plane is a counterpart of the q-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant.…
S. Cho, J. Madore, K. S. ParkAug 30, 1997
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Explicit Hopf-Galois description of SLe2iπ/3-induced Frobenius homomorphisms
The exact sequence of ``coordinate-ring'' Hopf algebras A(SL(2,C)) -> A(SLq(2)) -> A(F) determined by the Frobenius map Fr, and the same way obtained exact sequence of (quantum) Borel…
L. Dabrowski, P. M. Hajac, P. SiniscalcoAug 29, 1997
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Quantization of Equivariant Vector Bundles
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic…
Eli HawkinsAug 29, 1997
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The Casson-Walker-Lescop Invariant as a Quantum 3-manifold Invariant
We give a direct computational proof that the degree 1 part of the Le-Murakami-Ohtsuki invariant of a closed oriented 3-manifold M is determined by the Casson-Walker-Lescop invariant. Moreover, if…
Nathan Habegger, Anna BeliakovaAug 26, 1997
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Topics in hidden symmetries. VI
In this note devoted to some aspects of the inverse problem of representation theory the attention is concentrated on the interrelations between various algebraic structures (algebras with operators)…
Denis V. JurievAug 25, 1997
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Topics in isotopic pairs and their representations. III. Bunches of Lie algebras and modified classical Yang-Baxter equation
This third part of the series is a brief comment to certain aspects of the theory of classical r-matrix and bihamiltonian formalism, which motivations lie in constructions of the previous two parts.
Denis V. JurievAug 23, 1997
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On Quantum Orbit Method
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum…
Leonid I. KorogodskyAug 22, 1997
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Quantum Lorentz and braided Poincare groups
Quantum Lorentz groups H admitting quantum Minkowski space V are selected. Natural structure of a quantum space G = V x H is introduced, defining a quantum group structure on G only for triangular H…
S. ZakrzewskiAug 22, 1997
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Deformed Yangians and Integrable Models
Twisted Hopf algebra slξ(2) gives rise to a deformation of the Yangian Y(sl(2)). The corresponding deformations of the integrable XXX-spin chain and the Gaudin model are discussed.
P. P. Kulish, A. A. StolinAug 22, 1997
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