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Quantum Algebra papers — page 15

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Kazhdan-Lusztig tensoring and Harish-Chandra categories
We use the Kazhdan-Lusztig tensoring to define affine translation functors, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA, and to…
I. B. Frenkel, F. MalikovMar 5, 1997
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Bargmann representation for some deformed harmonic oscillators with non-Fock representation
We prove that Bargmann representations exist for some deformed harmonic oscillators that admit non-Fock representations. In specific cases, we explicitly obtain the resolution of the identity in…
M. Irac-Astaud, G. RideauMar 5, 1997
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Canonical basis and homology of local systems
Using the isomorphism between highest weight Uq(sl2)-modules and homologies of certain local systems on the configuration spaces, constructed by Varchenko, we give a geometric construction of the…
Igor Frenkel, Alexander Kirillov, Alexander VarchenkoMar 4, 1997
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Generalized Hermite Polynomials and the Heat Equation for Dunkl Operators
Based on the theory of Dunkl operators, this paper presents a general concept of multivariable Hermite polynomials and Hermite functions which are associated with finite reflection groups on $…
Margit RöslerMar 3, 1997
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On q-Analogues of Bounded Symmetric Domains and Dolbeault Complexes
A very well known result by Harish-Chandra claims that any Hermitian symmetric space of non-compact type admits a canonical embedding into a complex vector space V. The image of this embedding is a…
S. Sinel'shchikov, L. VaksmanMar 3, 1997
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Free coherent states and distributions on p-adic numbers
Free coherent states for a system with two degrees of freedom is defined. An isomorphism of the space of distributions on 2-adic disc and the space of free coherent states is constructed.
S. V. KozyrevMar 3, 1997
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Braided-Lie bialgebras
We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We…
S. MajidMar 3, 1997
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Row-reducing the quantum determinant and Dieudonne determinant
We prove that row reducing a quantum matrix yields another quantum matrix for the same parameter q. This means that the elements of the new matrix satisfy the same relations as those of the original…
Horia C. PopMar 3, 1997
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A generalization of Scheunert's Theorem on cocycle twisting of color Lie algebras
A classical theorem of Scheunert on G-color Lie algebras, asserts in the case of finitely generated abelian groups, one can twist the algebra structure and the commutation bicharacter on G by a…
Horia C. PopMar 2, 1997
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Twisting of monoidal structures
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal…
A. A. DavydovMar 1, 1997
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Cartan-Calculus and its Generalizations via a Path-Integral Approach to Classical Mechanics
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical…
Ennio GozziFeb 26, 1997
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Shadow of noncommutativity
We analyse the structure of the κ=0 limit of a family of algebras Aκ describing noncommutative versions of space-time, with κ a parameter of noncommutativity. Assuming the Poincaré covariance…
Michel Dubois-Violette, John Madore, Richard KernerFeb 25, 1997
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Contractions on the Classical Double
Lie algebra contractions on the classical Drinfel'd Double of a given Lie bialgebra are introduced and compared to the usual Lie bialgebra contraction theory. The connection between both…
Angel Ballesteros, Mariano del OlmoFeb 25, 1997
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Algebra of screening operators for the deformed Wn algebra
We construct a family of intertwining operators (screening operators) between various Fock space modules over the deformed Wn algebra. They are given as integrals involving a product of screening…
B. Feigin, M. Jimbo, T. Miwa et al.Feb 25, 1997
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Twisting 2-cocycles for the construction of new non-standard quantum groups
We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard…
Andrew D. Jacobs, J. F. CornwellFeb 24, 1997
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Twisted representations of vertex operator algebras and associative algebras
Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras Ag,n(V) with n∈1T nonnegative such that Ag,n(V) is a quotient…
C. Dong, H. Li, G. MasonFeb 21, 1997
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Twisted h-spacetimes and invariant equations
We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the…
J. A. de Azcárraga, P. P. Kulish, F. RodenasFeb 21, 1997
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Non-commutative Euclidean and Minkowski Structure
A noncommutative *-algebra that generalizes the canonical commutation relations and that is covariant under the quantum groups SOq(3) or SOq(1,3) is introduced. The generating elements of this…
A. Lorek, W. Weich, J. WessFeb 20, 1997
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Toroidal actions on level 1 modules of Uq(sln)
Recently Varagnolo and Vasserot established that the q-deformed Fock spaces due to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum toroidal algebra Uq(sln,tor) (n > 2) with…
Y. Saito, K. Takemura, D. UglovFeb 19, 1997
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Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral
Different analogs of quasiclassical limit for a q-oscillator which result in different (commutative and non-commutative) algebras of ``classical'' observables are derived. In particular, this…
M. Chaichian, A. Demichev, P. P. KulishFeb 18, 1997
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Difference Macdonald-Mehta Conjecture
In the paper we formulate and verify a difference counterpart of the Macdonald-Mehta conjecture and its generalization for the Macdonald polynomials. Namely, we determine the Fourier transforms of…
Ivan CherednikFeb 17, 1997
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A note on the trinomial analogue of Bailey's lemma
Recently, Andrews and Berkovich introduced a trinomial version of Bailey's lemma. In this note we show that each ordinary Bailey pair gives rise to a trinomial Bailey pair. This largely widens…
S. Ole WarnaarFeb 17, 1997
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On the algebraic structure of differential calculus on quantum groups
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum…
O. V. Radko, A. A. VladimirovFeb 14, 1997
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On q-Clebsch Gordan Rules and the Spinon Character Formulas for Affine C2(1) Algebra
A q-analog of the Clebsch Gordan rules for the tensor products of the fundamental representations of Yangian is introduced. Its relation to the crystal base theory and application to the spinon…
Yasuhiko YamadaFeb 14, 1997
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An example of a braided category of C*- algebras
A braided category of C*-algebras is constructed. Its objects are C*-algebras endowed with an action of the group R, its morphisms are C*-algebras morphisms intertwining the action of R, the crossed…
Malgorzata Rowicka-KudlickaFeb 13, 1997
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