Quantum E(2) groups and Lie bialgebra structuresLie bialgebra structures on e(2) are classified. For two Lie bialgebra structures which are not coboundaries (i.e. which are not determined by a classical r-matrix) we solve the cocycle…Jan Sobczyk·Mar 12, 1996SaveLearn
Kappa-contraction from SUq(2) to Eκ(2)We present contraction prescription of the quantum groups: from SUq(2) to Eκ(2). Our strategy is different then one chosen in ref. [P. Zaugg, J. Phys. A 28 (1995) 2589]. We provide…Jan Sobczyk·Mar 12, 1996SaveLearn
A Remark on the Higher Capelli IdentitiesA simple proof of the higher Capelli identities is given.A. Molev·Mar 12, 1996SaveLearn
Equivalence of q-bosons using the exponential phase operatorVarious forms of the q-boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator. Both the one-component and the multicomponent q-bosons are…S. U. Park·Mar 11, 1996SaveLearn
Generalized weight functions and the Macdonald polynomialsA weight function which q-generalizes the ground state wave function of the multi-component Calogero-Sutherland quantum many body system is introduced. Conjectures, and some proofs in special…T. H. Baker, P. J. Forrester·Mar 8, 1996SaveLearn
Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal AlgebraThe construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of Uq (su(2)) quantum affine Lie algebra and a single real Fermi field.…E. Batista, J. F. Gomes, I. J. Lautenschleguer·Mar 6, 1996SaveLearn
Beyond the `Pentagon Identity'An algebraical background of the Lattice Conformal Field Theory is refined with the help of a novel q-exponential identity.A. Yu. Volkov·Mar 6, 1996SaveLearn
Topological quantum field theory with corners based on the Kauffman bracketThe paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction…Razvan Gelca·Mar 6, 1996SaveLearn
A note on Connections and BimodulesWe discuss three problems related to connections on bimodules. These are left and right Leibniz rule for connections, left and right linearity of their curvatures and extension of connections to…Aristophanes Dimakis·Mar 1, 1996SaveLearn
Quasi-Classical Lie-Super Algebra and Lie-Super Triple SystemsNotions of quasi-classical Lie-super algebra as well as Lie-super triple systems have been given and studied with some examples. Its application to Yang-Baxter equation has also been given.Susumu Okubo, Noriaki Kamiya·Feb 29, 1996SaveLearn
The centre of the graph and moduli algebras at roots of 1The structure of the centres Z() and Z() of the graph algebra Lg(sl2) and the moduli algebra Mg(sl2) is studied at roots of 1. It it shown that $…S. A. Frolov·Feb 29, 1996SaveLearn
Metrics and Pairs of Left and Right Connections on BimodulesProperties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an…L. Dcabrowski, P. M. Hajac, G. Landi et al.·Feb 29, 1996SaveLearn
Exact Deformations of Quantum Groups; Applications to the Affine caseThis paper continues our investigation of a class of generalized quantum groups. The "standard" R-matrix was shown to be the unique solution of a very simple, linear recursion relation and…C. Frønsdal·Feb 28, 1996SaveLearn
The multiple gamma function and its q-analogueWe give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product formula) of the Vignéras multiple gamma function by considering the…Kimio Ueno, Michitomo Nishizawa·Feb 27, 1996SaveLearn
Deformed and extended Galilei group Hopf algebrasThe κ-deformed extended Galilei Hopf group algebra, Funκ( G(m)), is introduced. It provides an example of a cocycle bicrossproduct structure, and is shown to be the…J. A. de Azcarraga, J. C. Perez Bueno·Feb 22, 1996SaveLearn
Intertwining Operators for the Central Extension of the Yangian DoubleWe continue the investigation of the central extended Yangian double [S. Khoroshkin, q-alg/9602031]. In this paper we study the intertwining operators for certain infinite dimensional representations…S. Khoroshkin, D. Lebedev, S. Pakuliak·Feb 21, 1996SaveLearn
Central Extension of the Yangian DoubleCentral extension of the Double of the Yangian is defined for a simple Lie algebra g with complete proof for g =sl2. Basic representations and intertwining operators are…S. M. Khoroshkin·Feb 21, 1996SaveLearn
Lie bialgebra quantizations of the oscillator algebra and their universal R--matricesAll coboundary Lie bialgebras and their corresponding Poisson--Lie structures are constructed for the oscillator algebra generated by \å,,,\. Quantum oscillator algebras are derived from…Angel Ballesteros, Francisco J. Herranz·Feb 20, 1996SaveLearn
Young Basis, Wick Formula, and Higher Capelli IdentitiesWe prove Capelli type identities which involve the whole universal enveloping algebra U(gl(n)) and matrix elements of irreducible representations of the symmetric group. These identities generalize…Andrei Okounkov·Feb 19, 1996SaveLearn
Quantum Immanants and Higher Capelli IdentitiesWe consider remarkable central elements of the universal enveloping algebra of the general linear algebra which we call quantum immanants. We express them in terms of generators Eij and as…Andrei Okounkov·Feb 19, 1996SaveLearn
Tensor product of Vertex operator algebrasLet V1 V2 be a tensor product of VOAs. Using Zhu theory we discuss the theory of representations of V (associative algebra, modules and fusion rules). We prove that this theory is more or…Antun Milas·Feb 19, 1996SaveLearn
Canonical bases of q-deformed Fock spacesWe define a canonical basis of the q-deformed Fock space representation of the affine Lie algebra n. We conjecture that the entries of the transition matrix between this basis and the…Bernard Leclerc, Jean-Yves Thibon·Feb 16, 1996SaveLearn
Massey products and deformationsThe classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal…Dmitry Fuchs, Lynelle Lang·Feb 14, 1996SaveLearn
Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomialsUsing the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric 3-particle Ruijsenaars model (relativistic generalization of…Vadim B. Kuznetsov, Evgueni K. Sklyanin·Feb 13, 1996SaveLearn
Coalgebra Gauge TheoryWe develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which…T. Brzezinski, S. Majid·Feb 12, 1996SaveLearn