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Quantum Algebra papers — page 30

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Properties of some families of hypergeometric orthogonal polynomials in several variables
Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric…
Jan F. van DiejenApr 3, 1996
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Commuting difference operators with applications to orthogonal polynomials in several variables
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the…
J. F. van DiejenApr 3, 1996
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A system of difference equations with elliptic coefficients and Bethe vectors
An elliptic analogue of the q deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.
Takashi TakebeApr 3, 1996
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Bosonic representations of Yangian Double Y() with =N,N
On the basis of `RTT=TTR' formalism, we introduce the quantum double of the Yangian Y() for =N,N with a central extension. The Gauss decomposition of T-matrices…
Kenji IoharaApr 1, 1996
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A central extension of Y(2) and its vertex representations
A central extension of Y(2) is proposed. The bosonization of level 1 module and vertex operators are also given.
Kenji Iohara, Mika KohnoApr 1, 1996
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Some Remarks on Quantum and Braided Group Gauge Theory
We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the…
S. MajidMar 31, 1996
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Perfect Crystals and q-deformed Fock Spaces
A general scheme for the wedge construction of q-deformed Fock spaces using the theory of perfect crystals is presented. Let Uq() be a quantum affine algebra. Let V be a finite-dimensional…
Masaki Kashiwara, Tetsuji Miwa, Jens-Ulrik H. Petersen et al.Mar 29, 1996
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A supergeometric interpretation of vertex operator superalgebras
Huang's geometric interpretation of vertex operator algebras is extended to a supergeometric interpretation of vertex operator superalgebras. In particular, the geometry of spheres with punctures…
Katrina D. BarronMar 29, 1996
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Hom functor and the associativity of tensor products of modules for vertex operator algebras
We give a new, construction-free proof of the associativity of tensor product for modules for rational vertex operator algebras under certain convergence conditions.
Chongying Dong, Haisheng Li, Geoffrey MasonMar 29, 1996
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Symmetric and non-symmetric quantum Capelli polynomials
We define a family of symmetric and a family of non-symmetric polynomials in terms of vanishing conditions. These families depend on two paramters, q and t. Their main feature is that they consist of…
Friedrich KnopMar 29, 1996
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Integrality of two variable Kostka functions
The two variable Kostka functions are the scalar products of the Macdonald polynomials with the Schur polynomials with respect to the scalar product which makes the Hall-Littlewood polynomials…
Friedrich KnopMar 29, 1996
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Skew Symmetric Bundle Maps on Space-Time
We study the "Lie Algebra" of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points…
Daniel Henry GottliebMar 28, 1996
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Algebraic integrability of Macdonald operators and representations of quantum groups
In this paper we construct examples of commutative rings of difference operators with matrix coefficients from representation theory of quantum groups, generalizing the results of our previous paper…
Pavel Etingof, Konstantin StyrkasMar 25, 1996
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Interpolation between para-Bose and para-Fermi statistics
Using deformed Green's oscillators and Green's Ansatz,we construct a multiparameter interpolation between para-Bose and para-Fermi statistics of a given order. When the interpolating…
S. Meljanac, M. Milekovic, A. PericaMar 24, 1996
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Homological Reduction of Constrained Poisson Algebras
The ``classical BRST construction'' as developed by Batalin-Fradkin-Vilkovisky is a homological construction for the reduction of the Poisson algebra P = C∞ (W) of smooth functions on…
Jim StasheffMar 24, 1996
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On the D-module and formal-variable approaches to vertex algebras
In a program to formulate and develop two-dimensional conformal field theory in the framework of algebraic geometry, Beilinson and Drinfeld have recently given a notion of ``chiral algebra''…
Yi-Zhi Huang, James LepowskyMar 23, 1996
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Diagrammatics of Braided Group Gauge Theory
We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal…
S. MajidMar 22, 1996
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On the Connectivity of Cobordisms and Half-Projective TQFT's
We consider a generalization of the axioms of a TQFT, so called half-projective TQFT's, with an anomaly, xμ, in the composition law. μ is a coboundary on the cobordism categories with…
Thomas KerlerMar 22, 1996
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Crossed Products by a Coalgebra
We introduce the notion of a crossed product of an algebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result…
Tomasz BrzezinskiMar 18, 1996
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On the defining relations of the affine Lie superalgebras and their quantized universal enveloping superalgebras
In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a…
Hiroyuki YamaneMar 15, 1996
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Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians
We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group.…
M. Noumi, M. S. Dijkhuizen, T. SugitaniMar 15, 1996
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Finite type 3-manifold invariants and the structure of the Torelli group I
Using the recently developed theory of finite type invariants of integral homology 3-spheres we study the structure of the Torelli group of a closed surface. Explicitly, we construct (a) natural…
Stavros Garoufalidis, Jerome LevineMar 14, 1996
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Alexander-Conway limits of many Vassiliev weight systems
Previous work has shown that certain leading orders of arbitrary Vassiliev invariants are generically in the algebra of the coefficients of the Alexander-Conway polynomial KSA. Here we…
A. KrickerMar 14, 1996
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Hidden Symmetry of the Differential Calculus on the Quantum Matrix Space
A standard bicovariant differential calculus on a quantum matrix space Mat(m,n)q is considered. The principal result of this work is in observing that the $Uqs(glm×…
S. Sinel'shchikov, L. VaksmanMar 14, 1996
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Vassiliev knot invariants and Chern-Simons perturbation theory to all orders
At any order, the perturbative expansion of the expectation values of Wilson lines in Chern-Simons theory gives certain integral expressions. We show that they all lead to knot invariants. Moreover…
Daniel Altschuler, Laurent FreidelMar 12, 1996
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