Universal R-matrices for finite Abelian groups -- a new look at graded multilinear algebraThe universal R-matrices and, dually, the coquasitriangular structures of the group Hopf algebra of a finite Abelian group (resp. of an arbitrary Abelian group) are determined. This is used to…M. Scheunert·Aug 24, 1995SaveLearn
On the deformability of Heisenberg algebrasBased on the vanishing of the second Hochschild cohomology group of the enveloping algebra of the Heisenberg algebra it is shown that differential algebras coming from quantum groups do not provide a…Mathias Pillin·Aug 24, 1995SaveLearn
Twisted quantum affine algebras and solutions to the Yang-Baxter equationWe construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum…Gustav W. Delius, Mark D. Gould, Yao-Zhong Zhang·Aug 22, 1995SaveLearn
Quantum Lie algebras associated to Uq(gln) and Uq(sln)Quantum Lie algebras g are non-associative algebras which are embedded into the quantized enveloping algebras Uq(g) of Drinfeld and Jimbo in the same way as ordinary Lie algebras are…Gustav W. Delius, Mark D. Gould, Andreas Hüffmann et al.·Aug 22, 1995SaveLearn
Quantum WN Algebras and Macdonald PolynomialsWe derive a quantum deformation of the WN algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.H. Awata, H. Kubo, S. Odake et al.·Aug 21, 1995SaveLearn
Generalization of the h-Deformation to Higher DimensionsIn this article we construct GLh(3) from GLq(3) by a singular map. We show that there exist two singular maps which map GLq(3) to new quantum groups. We also construct their…M. Alishahiha·Aug 21, 1995SaveLearn
Quantum W-algebras and Elliptic AlgebrasWe define quantum W-algebras generalizing the results of Reshetikhin and the second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated to slN is an associative algebra…Boris Feigin, Edward Frenkel·Aug 17, 1995SaveLearn
Quantum Fibre Bundles. An IntroductionAn approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.Tomasz Brzezinski·Aug 17, 1995SaveLearn
On the Classification of quantum qroup stuctures on the group GL(2)All quantum group structures on the group GL(2) are classified. It is shown that there are only two such structures, the well known quantum groups GLqp(2) and GLhh'(2).A. Aghamohammadi, M. Khorrami, A. Shariati·Aug 17, 1995SaveLearn
Decomposition of q-deformed Fock spacesA decomposition of the level-one q-deformed Fock representations of is given. It is found that the action of on these Fock spaces is centralized by a Heisenberg algebra, which arises…Masaki Kashiwara, Tetsuji Miwa, Eugene Stern·Aug 14, 1995SaveLearn
Quantum categories. Quantization of the category of linear spacesWe define generalized bialgebras and Hopf algebras and on this basis we introduce quantum categories and quantum groupoids. The quantization of the category of linear (super)spaces is constructed. We…Theodore Voronov·Aug 11, 1995SaveLearn
Yangians: their Representations and CharactersWe give several formulas for the character of an arbitrary irreducible finite--dimensional representation for the Yangian of sl2.Vyjayanthi Chari, Andrew Pressley·Aug 10, 1995SaveLearn
Toda Fields on Riemann Surfaces: remarks on the Miura transformationWe point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field…Ettore Aldrovandi·Aug 5, 1995SaveLearn
Scattering matrices and affine Hecke algebrasWe construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke…Vincent Pasquier·Aug 1, 1995SaveLearn
Quantized Lax Equations and Their SolutionsIntegrable systems on quantum groups are investigated. The Heisenberg equations possessing the Lax form are solved in terms of the solution to the factorization problem on the corresponding quantum…B. Jurco, M. Schlieker·Aug 1, 1995SaveLearn
On Finiteness of Certain Vassiliev InvariantsThe best known examples of Vassiliev invariants are the coefficients of a Jones-type polynomial expanded after exponential substitution. We show that for a given knot, the first N Vassiliev…Louis H. Kauffman, Masahico Saito, Stephen Sawin·Jul 31, 1995SaveLearn
A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric FunctionsA quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra.…Jun'ichi Shiraishi, Harunobu Kubo, Hidetoshi Awata et al.·Jul 30, 1995SaveLearn
Self-dual Koornwinder-Macdonald polynomialsWe prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify…Jan F. van Diejen·Jul 28, 1995SaveLearn
Linear Connections on the Two Parameter Quantum PlaneWe apply a recently proposed definition of a linear connection in non commutative geometry based on the natural bimodule structure of the algebra of differential forms to the case of the…Y. Georgelin, T. Masson, J. -C. Wallet·Jul 27, 1995SaveLearn
A Relation Between the Kauffman and the HOMFLY Polynomials for Torus KnotsPolynomial invariants corresponding to the fundamental representation of the gauge group SO(N) are computed for arbitrary torus knots in the framework of Chern-Simons gauge theory making use of…J. M. F. Labastida, E. Perez·Jul 26, 1995SaveLearn
Submanifolds and Quotient Manifolds in Noncommutative GeometryWe define and study noncommutative generalizations of submanifolds and quotient manifolds, for the derivation-based differential calculus introduced by M.~Dubois-Violette and P.~Michor. We give…Thierry Masson·Jul 26, 1995SaveLearn
The gl(M|N) Super Yangian and Its Finite Dimensional RepresentationsMethods are developed for systematically constructing the finite dimensional irreducible representations of the super Yangian Y(gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown…R. B. Zhang·Jul 26, 1995SaveLearn
On the first order operators in bimodulesWe analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.Michel Dubois-Violette, Thierry Masson·Jul 25, 1995SaveLearn
New Solutions of the Yang-Baxter Equation Based on Root of 1 Representations of the Para-Bose Superalgebra Uq[osp(1/2)]New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum…T. D. Palev, N. I. Stoilova·Jul 25, 1995SaveLearn
Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1The unitarizable irreps of the deformed para-Bose superalgebra pBq, which is isomorphic to Uq[osp(1/2)], are classified at q being root of 1. New finite-dimensional irreps of Uq[osp(1/2)]…T. D. Palev, N. I. Stoilova·Jul 25, 1995SaveLearn