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Quantum Algebra papers — page 6

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Quantum Galois theory for finite groups
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set VG of…
Akihide Hanaki, Masahiko Miyamoto, Daisuke TambaraSep 29, 1997
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Kazhdan-Lusztig polynomials and canonical basis
In this paper we show that the Kazhdan-Lusztig polynomials (and, more generally, parabolic KL polynomials) for the group Sn coincide with the coefficients of the canonical basis in nth tensor…
Igor Frenkel, Mikhail Khovanov, Alexander KirillovSep 29, 1997
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Deformation quantization of Poisson manifolds, I
I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…
Maxim KontsevichSep 29, 1997
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On Fusion Algebras and Modular Matrices
We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using…
T. Gannon, M. A. WaltonSep 26, 1997
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Universal R-matrix Of The Super Yangian Double DY(gl(1|1))
Based on Drinfeld realization of super Yangian Double DY(gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another…
Jin-fang Cai, Shi-kun Wang, Ke Wu et al.Sep 25, 1997
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A coset-type construction for the deformed Virasoro algebra
An analog of the minimal unitary series representations for the deformed Virasoro algebra is constructed using vertex operators of the quantum affine algebra Uq(sl2). A similar construction…
Michio Jimbo, Jun'ichi ShiraishiSep 25, 1997
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q-deformed algebras Uq(son) and their representations
For the nonstandard q-deformed algebras Uq(son), defined recently in terms of trilinear relations for generating elements, most general finite dimensional irreducible representations directly…
A. M. Gavrilik, N. Z. IorgovSep 24, 1997
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Representations of the q-deformed algebra U'q(so2,2)
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible *-representations of the q-deformed algebra U'q(so2,2) which is a real…
A. U. KlimykSep 23, 1997
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Dual pairs and tensor categories of modules over Lie algebras gl∞ and W1 +∞
We introduce a tensor category O+ (resp. O-) of certain modules of gl∞ with non-negative (resp. non-positive) integral central charges with the usual tensor product. We also introduce a…
Weiqiang WangSep 23, 1997
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What is a vertex algebra?
These are the notes of an informal talk in Bonn describing how to define an analogue of vertex algebras in higher dimensions.
Richard E. BorcherdsSep 22, 1997
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Quantum Orthogonal Planes: ISOq,r(N) and SOq,r(N) -- Bicovariant Calculi and Differential Geometry on Quantum Minkowski Space
We construct differential calculi on multiparametric quantum orthogonal planes in any dimension N. These calculi are bicovariant under the action of the full inhomogeneous (multiparametric) quantum…
Paolo Aschieri, Leonardo Castellani, Antonio Maria ScarfoneSep 20, 1997
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Conjectured enumeration of Vassiliev invariants
A rational Ansatz is proposed for the generating function Σj,k β2j+k,2jxj yk, where βm,u is the number of primitive chinese character diagrams with u univalent and 2m-u…
D. J. BroadhurstSep 20, 1997
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Meromorphic tensor categories
We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld,…
Yan SoibelmanSep 19, 1997
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Feynman Integral, Knot Invariant and Degree Theory of Maps
The universal Vassiliev invariant from the perturbative Chern-Simons theory is actually a knot invariant without any correction term. The anomaly considered by Bott and Taubes is proved to be zero.
Su-Win YangSep 19, 1997
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8-Vertex Correlation Functions and Twist Covariance of q-KZ Equation
We study the vertex operators Φ(z) associated with standard quantum groups. The element Z = RRt is a "Casimir operator" for quantized Kac-Moody algebras and the quantum…
C. Fronsdal, A. GalindoSep 18, 1997
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Formal distribution algebras and conformal algebras
Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments…
Victor G. KacSep 17, 1997
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The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl(2)-Modules
We consider the quantized Knizhnik-Zamolodchikov difference equation (qKZ) with values in a tensor product of irreducible sl(2) modules, the equation defined in terms of rational R-matrices. We solve…
E. Mukhin, A. VarchenkoSep 16, 1997
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Quantum and braided group Riemannian geometry
We formulate quantum group Riemannian geometry as a gauge theory of quantum differential forms. We first develop (and slightly generalise) classical Riemannian geometry in a self-dual manner as a…
S. MajidSep 16, 1997
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Three Short Distance Structures from Quantum Algebras
We review known and we present new results on three types of short distance structures of observables which typically appear in studies of quantum group related algebras. In particular, one of the…
A. KempfSep 15, 1997
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σ-models on the quantum group manifolds SLq(2,R), SLq(2,R)/Uh(1), Cq(2|0) and infinitesimal trasformations
The differential and variational calculus on the SLq(2,R) group is constructed. The spontaneous breaking symmetry in the WZNW model with SLq(2,R) quantum group symmetry and in the…
V. D. GershunSep 15, 1997
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Dynamically twisted algebra Aq,p;π(gl2) as current algebra generalizing screening currents of q-deformed Virasoro algebra
In this paper, we propose an elliptic algebra Aq,p;π(gl2) which is based on the relations RLL=LLR*, where R and R* are the dynamical R-maxtrices of A(1)1 type face…
B. Y. Hou, W. L. YangSep 13, 1997
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On Vassiliev Invariants for Links in Handlebodies
The notion of Vassiliev algebra in case of hanlebodies is developed. The analogues of the results of John Baez for links in handlebodies are proved. That means that there exists a one-to-one…
V. V. VershininSep 13, 1997
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A Star Product for Complex Grasmann Manifolds
We explicitly construct a star product for the complex Grassmann manifolds using the method of phase space reduction. Functions on C(p+q)· p~*, the space of (p+q)× p matrices…
Joachim SchirmerSep 13, 1997
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Integrals for braided Hopf algebras
Let H be a Hopf algebra in a rigid braided monoidal category with split idempotents. We prove the existence of integrals on (in) H characterized by the universal property, employing results about…
Yuri Bespalov, Thomas Kerler, Volodymyr Lyubashenko et al.Sep 12, 1997
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Extensions of conformal modules
In this paper we classify extensions between irreducible finite conformal modules over the Virasoro algebra, over the current algebras and over their semidirect sums.
Shun-Jen Cheng, Victor Kac, Minoru WakimotoSep 12, 1997
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