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Quantum Algebra papers — page 27

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Quantization of geometry associated to the quantized Knizhnik-Zamolodchikov equations
It is known that solutions of the Knizhnik-Zamolodchikov differential equations are given by integrals of closed differential forms over suitable cycles. In this paper a quantization of this…
Alexander VarchenkoJun 5, 1996
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Solutions of the elliptic qKZB equations and Bethe ansatz I
We give an integral representation for solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, in the case of sl(2). The result is based on a geometric construction of…
Giovanni Felder, Alexander Varchenko, Vitaly TarasovJun 5, 1996
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Equivalence of Two Approaches to the mKdV Hierarchies
The equivalence between the approaches of Drinfeld-Sokolov and Feigin-Frenkel to the mKdV hierarchies is established. A new derivation of the mKdV equations in the zero curvature form is given.…
Benjamin Enriquez, Edward FrenkelJun 5, 1996
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Nonstandard Poincare and Heisenberg Algebras
New deformations of the Poincare group Fun(P(1+1)) and its dual enveloping algebra U(p(1+1)) are obtained as a contraction of the h-deformed (Jordanian) quantum group Fun(SLh(2)) and its…
Preeti ParasharJun 4, 1996
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Abstract carrier space formalism for the irreducible tensor operators of compact quantum group algebras
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract…
J. F. CornwellJun 4, 1996
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Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras
The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentions of compact quantum group algebras are deduced first in both the right and left…
J. F. CornwellJun 3, 1996
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Hecke symmetries and characteristic relations on Reflection Equation algebras
We discuss how properties of Hecke symmetry (i.e., Hecke type R-matrix) influence the algebraic structure of the corresponding Reflection Equation (RE) algebra. Analogues of the Newton relations and…
D. I. Gurevich, P. N. Pyatov, P. A. SaponovJun 2, 1996
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A level-one representation of the quantum affine superalgebra q(sl(M+1|N+1))
A level-one representation of the quantum affine superalgebra q(sl(M+1|N+1)) and vertex operators associated with the fundamental representations are constructed in terms of free…
K. Kimura, J. Shiraishi, J. UchiyamaJun 2, 1996
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Free Field Representation of Level-k Yangian Double DY(sl2)k and Deformation of Wakimoto Modules
Free field representation of level-k (=0,-2) Yangian double DY(sl2)k and a corresponding deformation of Wakimoto modules are presented. We also realize two types of vertex operators…
Hitoshi KonnoMay 30, 1996
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Some automorphisms of Generalized Kac-Moody algebras
To any symmetry of the Cartan matrix of a Generalized Kac-Moody (GKM) algebra we associate a family of automorphisms of the algebra which act in a natural way on the modules of the GKM algebra. We…
J"urgen Fuchs, Urmie Ray, Christoph SchweigertMay 30, 1996
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Quantum double of a (locally) compact group
We generalise the quantum double construction of Drinfel'd to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the *-algebra…
T. H. Koornwinder, N. M. MullerMay 29, 1996
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A new construction of the semi-infinite BGG resolution
We introduce the techniques of semiregular bimodules over a Lie algebra with respect to a Lie subalgebra. Using this techniques in the case of affine Lie algebras we introduce twisting functors on…
Sergey ArkhipovMay 29, 1996
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Shifted Schur Functions
The classical algebra Λ of symmetric functions has a remarkable deformation Λ*, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a distinguished basis…
Andrei Okounkov, Grigori OlshanskiMay 28, 1996
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Representation theory of deformed oscillator algebras
The representation theory of deformed oscillator algebras, defined in terms of an arbitrary function of the number operator~N, is developed in terms of the eigenvalues of a Casimir operator~C. It…
C. Quesne, N. VansteenkisteMay 28, 1996
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q-Krawtchouk polynomials as spherical functions on the Hecke algebra of type B
The generic Hecke algebra for the hyperoctahedral group, i.e. the Weyl group of type B, contains the generic Hecke algebra for the symmetric group, i.e. the Weyl group of type A, as a subalgebra.…
H. T. KoelinkMay 28, 1996
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Traces of Intertwining Operators for the Yangian Double
The traces over infinite dimensional representations of the central extended Yangian double for the product of operators which intertwine these representations are calculated. For the special…
S. Khoroshkin, D. Lebedev, S. PakuliakMay 28, 1996
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On Quantum Groups Co-Representations
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space…
H. Montani, R. TrincheroMay 24, 1996
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On the Deformation Quantization of super-Poisson Brackets
We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to…
Martin BordemannMay 24, 1996
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Casson-Lin's invariant of a knot and Floer homology
A. Casson defined an intersection number invariant which can be roughly thought of as the number of conjugacy classes of irreducible representations of π1(Y) into SU(2) counted with signs, where…
Weiping LiMay 22, 1996
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Squared Hopf algebras and reconstruction theorems
Given an abelian k-linear rigid monoidal category V, where k is a perfect field, we define squared coalgebras as objects of cocompleted V tensor V (Deligne's tensor product of categories)…
Volodymyr V. LyubashenkoMay 22, 1996
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Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity
We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th polynomial and the orthogonality measure are…
V. Spiridonov, A. ZhedanovMay 21, 1996
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q-Ultraspherical polynomials for q a root of unity
Properties of the q-ultraspherical polynomials for q being a primitive root of unity are derived using a formalism of the soq(3) algebra. The orthogonality condition for these polynomials…
V. Spiridonov, A. ZhedanovMay 21, 1996
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Certain associative algebras similar to U(sl2) and Zhu's algebra A(VL)
It is proved that Zhu's algebra for vertex operator algebra associated to a positive-definite even lattice of rank one is a finite-dimensional semiprimitive quotient algebra of certain…
Chongying Dong, Haisheng Li, Geoffrey MasonMay 21, 1996
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(2+1) null-plane quantum Poincaré group from a factorized universal R-matrix
The non-standard (Jordanian) quantum deformations of so(2,2) and (2+1) Poincaré algebras are constructed by starting from a quantum sl(2,) basis such that simple factorized expressions for…
Angel Ballesteros, Francisco J. HerranzMay 20, 1996
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Separation of variables for Gaudin-Calogero systems
We construct an elliptic analogue of Sklyanin's separation of variables for the sl(2) Gaudin system, using an adaptation of Drinfeld's Radon transformations.
B. Enriquez, B. Feigin, V. RubtsovMay 20, 1996
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