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Quantum Algebra papers — page 12

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L operators and Drinfeld's generators
Utilizing the multiplicative formula of universal R matrix, the correspondence between the L operators and Drinfeld's generators is explicitly calculated for quantum group Uq(g) with…
Norifumi Hayaishi, Kei MikiMay 26, 1997
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Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations
The elliptic quantum Knizhnik-Zamolodchikov-Bernard (qKZB) difference equations associated to the elliptic quantum group Eτ,η(sl2) is a system of difference equations with values in a tensor…
Giovanni Felder, Vitaly Tarasov, Alexander VarchenkoMay 26, 1997
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Geometry of Quantum Homogeneous Vector Bundles and Representation Theory of Quantum Groups I
Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited…
A. R. Gover, R. B. ZhangMay 26, 1997
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The Affine q-Schur algebra
We introduce an analogue of the q-Schur algebra associated to Coxeter systems of type An-1. We give two constructions of this algebra. The first construction realizes the algebra as a…
R. M. GreenMay 23, 1997
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On the tensor product construction for q-differential algebras
We show that for q=-1 the q-graded tensor product fails to preserve the q-differential structure of the product algebra and therefore there is no natural tensor product construction for…
Andrzej SitarzMay 23, 1997
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BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle
The quantum double for the quantized BRST superalgebra is studied. The corresponding R-matrix is explicitly constucted. The Hopf algebras of the double form an analytical variety with coordinates…
V. D. Lyakhovsky, V. I. TkachMay 18, 1997
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Poisson structures on the center of the elliptic algebra Ap,q(sl(2)c)
It is shown that the elliptic algebra Ap,q(sl(2)c) has a non trivial center at the critical level c=-2, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric…
J. Avan, L. Frappat, M. Rossi et al.May 16, 1997
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On Skein Algebras And Sl2(C)-Character Varieties
This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special…
Jozef H. Przytycki, Adam S. SikoraMay 15, 1997
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Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra sl(N)
The decompositions of the Fock and Basic modules of the affine Lie algebra sl(N) into irreducible submodules of the Yangian algebra Y(gl(N)) are constructed. Each of the irreducible submodules…
Denis UglovMay 14, 1997
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An Introduction to n-Categories
An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing…
John C. BaezMay 13, 1997
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The space of 3-manifolds and Vassiliev finite-type invariants
In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to…
Nadya ShirokovaMay 9, 1997
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Quantization of Poisson structures on 2
An 'isomorphism' between the 'moduli space' of star products on 2 and the 'moduli space' of all formal Poisson structures on 2 is established.
Dmitry TamarkinMay 9, 1997
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Separation of variables and integral relations for special functions
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new…
Vadim B. Kuznetsov, Evgueni K. SklyaninMay 8, 1997
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The Noncommutative Inhomogeneous Hopf Algebra
From the bicovariant first order differential calculus on inhomogeneous Hopf algebra B we construct the set of right-invariant Maurer-Cartan one-forms considered as a right-invariant basis…
M. Lagraa, N. TouhamiMay 7, 1997
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Finite type invariants III: manifold weight systems
We introduce the notion of weight system for finite type invariants of integral homology 3-spheres, and we show that invariants of type m are determined, modulo invariants of type m-1, by their…
Stavros Garoufalidis, Tomotada OhtsukiMay 7, 1997
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On some quadratic algebras
We study some quadratic algebras which are appeared in the low-dimensional topology and Schubert calculus. We introduce the Jucys-Murphy elements in the braid algebra and in the pure braid group, as…
Anatol N. KirillovMay 6, 1997
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Some IHX type relations on trivalent graphs and symplectic representation theory
We consider several algebras that arise in the study of the mapping class group (by means of topology and Hodge theory) and describe their symplectic-invariant parts in terms of algebras on trivalent…
Stavros Garoufalidis, Hiroaki NakamuraMay 5, 1997
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Algèbre homologique des N-complexes et homologie de Hochschild aux racines de l'unité
We set up a homological algebra for N-complexes, which are graded modules together with a degree -1 endomorphism d satisfying dN=0. We define Tor- and Ext-groups for N-complexes and we compute them…
Christian Kassel, Marc WambstMay 2, 1997
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Semi-Infinite Induction and Wakimoto Modules
The purpose of this paper is to suggest the construction and study properties of semi-infinite induction, which relates to semi-infinite cohomology the same way induction relates to homology and…
Alexander A. VoronovApr 29, 1997
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Configuration Space Integrals and Universal Vassiliev Invariants over Closed Surfaces
We show the existence of a universal Vassiliev invariant for links in closed surface cylinders by explicit construction using configuration space integrals.
Jørgen Ellegaard Andersen, Josef MattesApr 29, 1997
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Note on the Algebra of Screening Currents for the Quantum Deformed W-Algebra
With slight modifications in the zero modes contributions, the positive and negative screening currents for the quantum deformed W-algebra Wq,p(g) can be put together to form a single algebra…
Liu Zhao, Bo-Yu HouApr 27, 1997
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On Denominators of the Kontsevich Integral and the Universal Perturbative Invariant of 3-Manifolds
The integrality of the Kontsevich integral and perturbative invariants is discussed. We show that the denominator of the degree n part of the Kontsevich integral of any knot or link is a divisor of…
Thang T. Q. LeApr 25, 1997
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Bilinear generating functions for orthogonal polynomials
Using realisations of the positive discrete series representations of the Lie algebra su(1,1) in terms of Meixner-Pollaczek polynomials, the action of su(1,1) on Poisson kernels of these polynomials…
H. T. Koelink, J. Van der JeugtApr 24, 1997
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Screenings and a universal Lie-de Rham cocycle
Feigin and Fuchs have given a well-known construction of intertwining operators between "Fock-type" modules over the Virasoro algebra. The intertwiners are obtained via contour integration of…
Victor Ginzburg, Vadim SchechtmanApr 19, 1997
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Quantum Homogeneous Spaces and Coalgebra Bundles
It is shown that quantum homogeneous spaces of a quantum group H can be viewed as fibres of quantum fibrations with the total space H that are dual to coalgebra bundles. As concrete examples of such…
Tomasz BrzezinskiApr 19, 1997
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