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Quantum Algebra papers — page 41

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The q-Euclidean algebra Uq(eN) and the corresponding q-Euclidean lattice
We review the Euclidean Hopf algebra Uq(eN) dual of Fun(qN SOq-1(N)) and describe its fundamental Hilbert space representations fioeu, which turn out to be rather…
Gaetano FioreJul 1, 1995
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On Some Generalizations of Batalin-Vilkovisky Algebras
We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes…
Füsun AkmanJun 29, 1995
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Classical Limits, Quantum Duality and Lie-Poisson Structures
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is…
V. D. LyakhovskyJun 27, 1995
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Type-I Quantum Superalgebras, q-Supertrace and Two-variable Link Polynomials
A new general eigenvalue formula for the eigenvalues of Casimir invariants, for the type-I quantum superalgebras, is applied to the construction of link polynomials associated with any finite…
Mark D. Gould, Jon R. Links, Yao-Zhong ZhangJun 27, 1995
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Schur duality in the toroidal setting
The goal of the present paper is to prove with simple algebraic methods a Schur duality between Cherednik's double affine Hecke algebra of type GL(l) and the toroidal quantum group of type…
M. Varagnolo, E. VasserotJun 27, 1995
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Crystallized structure for level 0 part of modified quantum affine algebra
Crystal base of the level 0 part of the modified quantum affine algebra Uq(sl2)0 is given by path. Weyl group actions, extremal vectors and crystal structure of all…
Toshiki NakashimaJun 26, 1995
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Intertwining operators and Hirota bilinear equations
An interpretation of Hirota bilinear relations for classical τ functions is given in terms of intertwining operators. Noncommutative example of Uq(sl2) is presented.
S. Kharchev, S. Khoroshkin, D. LebedevJun 26, 1995
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Reduced Schur Functions and the Littlewood-Richardson Coefficients
The reduced Schur functions are studied. Their relations to the basic representation of A(1)r-1 and modular representations of the symmetric groups are clarified. Littlewood-Richardson…
Susumu Ariki, Tatsuhiro Nakajima, Hiro-Fumi YamadaJun 26, 1995
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Integration on quantum Euclidean space and sphere in N dimensions
Invariant integrals of functions and forms over q - deformed Euclidean space and spheres in N dimensions are defined and shown to be positive definite, compatible with the star - structure and to…
Harold SteinackerJun 23, 1995
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Eigenvalus of Casimir Invariants for Type-I Quantum Superalgebras
We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.
Mark D. Gould, Jon R. Links, Yao-Zhong ZhangJun 23, 1995
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On Quantum Lie Algebras and Quantum Root Systems
As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras Lq(g). We define these in terms of certain adjoint submodules of quantized enveloping…
Gustav W. Delius, Andreas HueffmannJun 22, 1995
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On the Cremmer-Gervais quantizations of SL(n)
Non-standard quantum groups CR [GL(n)] and CR [SL(n)] are constructed for a two parameter version of the Cremmer-Gervais R-matrix. An epimorphism is constructed from CR [GL(n)] onto the…
Timothy J. HodgesJun 22, 1995
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Level-0 structure of level-1 Uq(sl2)-modules and Macdonald polynomials
The level-1 integrable highest weight modules of Uq(sl2) admit a level-0 action of the same algebra. This action is defined using the affine Hecke algebra and the basis of the…
M. Jimbo, R. Kedem, H. Konno et al.Jun 16, 1995
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Nonstandard Quantum Groups and Superisation
We obtain the universal R-matrix of the non-standard quantum group associated to the Alexander-Conway knot polynomial. We show further that this non-standard quantum group is related to the…
S. Majid, M. J. Rodriguez-PlazaJun 13, 1995
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Cohomological construction of quantized universal enveloping algebras
Given an associative algebra A, and the category, , of its finite dimensional modules, additional structures on the algebra A induce corresponding ones on the category . Thus, the…
J. Donin, S. ShniderJun 12, 1995
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q-Gauge Theory
We examine some issues that arise in the q-deformation of a gauge theory. If the deformation is carried out by replacing the equal time commutators of free fields by the corresponding q-commutators,…
Robert J. FinkelsteinJun 12, 1995
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On Finite Type 3-Manifold Invariants II
This paper continues the study of finite-type invariants of homology spheres studied by Ohtsuki and Garoufalidis. We apply the surgery classification of links to give a diagrammatic description,…
Stavros Garoufalidis, Jerome LevineJun 12, 1995
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Localization of u-modules. IV. Localization on P1
This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of m finite factorizable sheaves \k\, we construct here some perverse sheaves over configuration…
M. Finkelberg, V. SchechtmanJun 9, 1995
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Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras
Differential calculi of Poincare-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of…
R. Martini, G. F. Post, P. H. M. KerstenJun 9, 1995
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Vassiliev Invariants for Torus Knots
Vassiliev invariants up to order six for arbitrary torus knots \ n , m \, with n and m coprime integers, are computed. These invariants are polynomials in n and m whose degree coincide…
M. Alvarez, J. M. F. LabastidaJun 9, 1995
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Integral Representations of the Macdonald Symmetric Functions
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
Hidetoshi Awata, Satoru Odake, Jun'ichi ShiraishiJun 8, 1995
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Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum Groups Related to Them
We study the problem of classifying all Poisson-Lie structures on the group G∞ of formal diffeomorphisms of the real line 1 which leave the origin fixed, as well as the extended…
Ognyan StoyanovJun 8, 1995
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Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group
A local classification of all Poisson-Lie structures on an infinite-dimensional group G∞ of formal power series is given. All Lie bialgebra structures on the Lie algebra G∞…
Boris Kupershmidt, Ognyan StoyanovJun 8, 1995
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Quantization of Lie bialgebras, I
In the paper "On some unsolved problems in quantum group theory", V.Drinfeld formulated the problem of the existence of a universal quantization for Lie bialgebras. When the paper "Tensor…
Pavel Etingof, David KazhdanJun 6, 1995
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On Deformations of Commutation Relation Algebras
This paper is on C - symmetric creation and annihilation operators, which are constructed on Wick's algebras which fulfil consistency conditions. The essential assumption is that every…
Robert RałowskiJun 6, 1995
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