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Quantum Algebra papers — page 44

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Cycles for asymptotic solutions and Weyl group
In this paper cycles for asymptotic solutions for Heckman-Opdam hypergeometric system of type An are described. Cycles are enumerated by elements of symmetric group. Leading asymptotic and leading…
A. Kazarnovski-KrolApr 20, 1995
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Bases of Bethe Vectors and Difference Equations with Regular Singular Points
We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight gl2-modules or Uq(gl2)-modules. We apply this result to difference equations with regular…
Vitaly Tarasov, Alexander VarchenkoApr 20, 1995
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A Quantum Analogue of the Z Algebra
We define a natural quantum analogue for the Z algebra, and which we refer to as the Zq algebra, by modding out the Heisenberg algebra from the quantum affine algebra…
A. Hamid Bougourzi, Luc VinetApr 19, 1995
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Simple currents and extensions of vertex operator algebras
We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are simple currents associated with semisimple weight one…
Chongying Dong, Haisheng Li, Geoffrey MasonApr 14, 1995
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Comments on Bosonisation and Biproducts
We clarify the relation between the `bosonisation' construction (due to the author) which can be used to turn a Hopf algebra B in the category of H-modules or H-comodules into an equivalent…
S. MajidApr 13, 1995
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Representations of Uq(sl(N)) at Roots of Unity
The Gelfand--Zetlin basis for representations of Uq(sl(N)) is improved to fit better the case when q is a root of unity. The usual q-deformed representations, as well as the nilpotent,…
B. Abdesselam, D. Arnaudon, A. ChakrabartiApr 12, 1995
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Yangian Construction of the Virasoro Algebra
We show that a Yangian construction based on the algebra of an infinite number of harmonic oscillators (i.e. a vibrating string) terminates after one step, yielding the Virasoro algebra.
S. Z. Levendorskii, A. SudberyApr 11, 1995
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The Robinson-Schensted correspondence as the quantum straightening at q=0
We show that the quantum straightening algorithm for Young tableaux and Young bitableaux reduces in the crystal limit q 0 to the Robinson-Schensted algorithm.
B. Leclerc, J. -Y. ThibonApr 7, 1995
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The quantum 2-sphere as a complex quantum manifold
We describe the quantum sphere of Podleś for c=0 by means of a stereographic projection which is analogous to that which exhibits the classical sphere as a complex manifold. We show that the…
Chong-Sun Chu, Pei-Ming Ho, Bruno ZuminoApr 6, 1995
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Quantization of quadratic Poisson brackets on a polynomial algebra of three variables
Poisson brackets (P.b) are the natural initial terms for the deformation quantization of commutative algebras. There is an open problem whether any Poisson bracket on the polynomial algebra of n…
J. Donin, L. Makar-LimanovApr 5, 1995
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Reconstruction of Weak Quasi Hopf Algebras
All rational semisimple braided tensor categories are representation categories of weak quasi Hopf algebras. To proof this result we construct for any given category of this kind a weak quasi tensor…
Reinhard HäringApr 3, 1995
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Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
We examine the two parameter deformed superalgebra Uqs(sl(1|2)) and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre…
D. Arnaudon, C. Chryssomalakos, L. FrappatMar 31, 1995
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Connections on central bimodules
We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is…
Michel Dubois-Violette, Peter W. MichorMar 31, 1995
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Representations of Quantum Affine Algebras
In this paper we define a quantum version of the ``fusion'' tensor product of two representations of an affine Kac-Moody algebra.It is replaced by what we call fusion action of the category…
D. Kazhdan, Y. SoibelmanMar 31, 1995
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Quadratic Poisson brackets and Drinfeld theory for associative algebras
The paper is devoted to the Poisson brackets compatible with multiplication in associative algebras. These brackets are shown to be quadratic and their relations with the classical Yang--Baxter…
A. A. Balinsky, Yu. M. BurmanMar 31, 1995
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Finite Group Factorisations and Braiding
We compute the quantum double, braiding and other canonical Hopf algebra constructions for the bicrossproduct Hopf algebra H associated to the factorization of a finite group into two subgroups.…
E. Beggs, J. Gould, S. MajidMar 30, 1995
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Geometry of Deformed Boson Algebras
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the q-- and the qp--deformed algebras arise as special cases are studied. Quantum…
P. Crehan, T. G. HoMar 30, 1995
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Representation Theory of Chern Simons Observables
Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the…
A. Yu. Alekseev, V. SchomerusMar 29, 1995
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Vectors and covectors in non-commutative setting
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors…
G. N. Parfionov, Yu. A. Romashev, R. R. ZapatrineMar 28, 1995
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Representations of knot groups and Vassiliev invariants
We show that the number of homomorphisms from a knot group to a finite group G cannot be a Vassiliev invariant, unless it is constant on the set of (2,2p+1) torus knots. In several cases, such as…
Daniel AltschulerMar 27, 1995
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Dual Structures in Non-Commutative Differential Algebras
The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is…
G. N. Parfionov, R. R. ZapatrinMar 24, 1995
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Quasi-* Structure on q-Poincare algebras
We use braided groups to introduce a theory of *-structures on general inhomogeneous quantum groups, which we formulate as quasi-* Hopf algebras. This allows the construction of the tensor…
S. MajidMar 23, 1995
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Localization of u-modules. III. Tensor categories arising from configuration spaces
This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number ζ an abelian artinian category . We…
M. Finkelberg, V. SchechtmanMar 22, 1995
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The Trivial Connection Contribution to Witten's Invariant and Finite Type Invariants of Rational Homology Spheres
We derive an analog of Melvin-Morton bound on the power series expansion of Jones polynomial of algebraically split links and boundary links. This allows us to produce a simple formula for the…
L. RozanskyMar 21, 1995
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Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity
We consider a special class of Kauffman's graph invariants of rigid vertex isotopy (graph invariants of Vassiliev type). They are given by a functor from a category of colored and oriented graphs…
Nobuharu HayashiMar 21, 1995
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