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Quantum Algebra papers — page 34

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On Nonlinear Angular Momentum Theories, Their Representations and Associated Hopf Structures
Nonlinear sl(2) algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a…
B. Abdesselam, J. Beckers, A. Chakrabarti et al.Jan 2, 1996
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Woven Braids and their Closures
A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or…
Jan A. KneisslerDec 31, 1995
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Recursively minimally-deformed oscillators
A recursive deformation of the boson commutation relation is introduced. Each step consists of a minimal deformation of a commutator [a,]=fk(·s;) into…
J. Katriel, C. QuesneDec 28, 1995
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Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties
We introduce a new family of symmetric functions, which are q-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock…
Alain Lascoux, Bernard Leclerc, Jean-Yves ThibonDec 27, 1995
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Tensor operators in R-matrix approach
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in…
Andrei G. BytskoDec 25, 1995
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Ruijsenaars' commuting difference operators as commuting transfer matrices
For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation…
Koji HasegawaDec 25, 1995
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Some Comments on Bosonisation and Biproducts
We collect here some less well-known results and formulae about the bosonisation construction which turns braided groups into quantum groups. We clarify the relation with biproduct Hopf algebras (the…
S. MajidDec 25, 1995
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Kostka Polynomials and Energy Functions in Solvable Lattice Models
The relation between the charge of Lascoux-Schuzenberger and the energy function in solvable lattice models is clarified. As an application, A.N.Kirillov's conjecture on the expression of the…
Atsushi Nakayashiki, Yasuhiko YamadaDec 24, 1995
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Decomposition of the adjoint representation of the small quantum sl2
Given a finite type root datum and a primitive root of unity q=[l]1, G.~Lusztig has defined in [Lu] a remarkable finite dimensional Hopf algebra over the cyclotomic field $…
V. OstrikDec 23, 1995
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The algebra of q-pseudodifferential symbols and the q-WKPn algebra
In this paper we continue with the program to explore the topography of the space of W-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko and Roger on the…
Javier Mas, Marcos SecoDec 22, 1995
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Intertwining Operator Algebras, Genus-Zero Modular Functors and Genus-Zero Conformal Field Theories
We describe the construction of the genus-zero parts of conformal field theories in the sense of G. Segal from representations of vertex operator algebras satisfying certain conditions. The…
Yi-Zhi HuangDec 22, 1995
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A New Deformed Supersymmetric Oscillator
We construct and discuss the Fock-space representation for a deformed oscillator with "peculiar" statistics. We show that corresponding algebra represents deformed supersymmetric oscillator.
S. Meljanac, M. Milekovic, A. PericaDec 21, 1995
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The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)
We introduce a universal R matrix for the Jordanian deformation of (2). Using (4)=(2) U-h((2)), we obtain the universal R matrix for (4).…
A. Shariati, A. Aghamohammadi, M. KhorramiDec 21, 1995
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Remarks on Geometric Quantization of R-matrix Type Poisson Brackets
We check The Vaisman condition of geometric quantization for R-matrix type Poisson pencil on a coadjoint orbit of a compact Lie group. It is shown that this condition isn't satisfied.
Kotov AlexeyDec 21, 1995
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Graded Contractions of Affine Kac-Moody Algebras
The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of…
Marc de MontignyDec 20, 1995
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Subalgebras with Converging Star Products in Deformation Quantization: An Algebraic Construction for Pn
Based on a closed formula for a star product of Wick type on n, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star-algebra…
M. Bordemann, M. Brischle, C. Emmrich et al.Dec 20, 1995
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The Kappa-Weyl group and its algebra
The κ-Poincare group and its algebra in an arbitrary basis are constructed. The κ-de\-formation of the Weyl group and its algebra in any dimensions and in the reference frame in which g00=0…
Piotr Kosinski, Pawel MaslankaDec 20, 1995
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Quantum group covariant systems
The meaning of quantum group transformation properties is discussed in some detail by comparing the (co)actions of the quantum group with those of the corresponding Lie group, both of which have the…
M. Chaichian, P. P. KulishDec 20, 1995
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Sugawara Construction and Casimir Operators for Krichever-Novikov Algebras
We show how to obtain from highest weight representations of Krichever-Novikov algebras of affine type (also called higher genus affine Kac-Moody algebras) representations of centrally extended…
Martin Schlichenmaier, Oleg K. SheinmanDec 18, 1995
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On Commutation Relations for Quons
The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum…
Wladyslaw MarcinekDec 15, 1995
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L-infinity algebras and their cohomology
An associative algebra is nothing but an odd quadratic codifferential on the tensor coalgebra of a vector space, and an A-infinity algebra is simply an arbitrary odd codifferential. Hochschild…
Michael PenkavaDec 12, 1995
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Antiholomorphic representations for orthogonal and symplectic quantum groups
The coadjoint orbits for the series Bl,\ Cl and Dl are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of…
P. StovicekDec 12, 1995
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Geometrical Quantization in Fock Space
We investigate an infinite dimensional analog of the theory of Lagrangian manifolds with complex germs. To such a manifold we assign a canonical operator that depends on creation and annihilation…
V. P. Maslov, O. Yu. ShvedovDec 9, 1995
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Compatible Poisson-Lie structures on the loop group of SL2
We define a 1-parameter family of r-matrices on the loop algebra of sl2, defining compatible Poisson structures on the associated loop group, which degenerate into the rational and…
B. Enriquez, V. N. RubtsovDec 8, 1995
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Kadell's two conjectures for Macdonald polynomials
This paper contains the proof of difference counterparts of the conjectures due to Keven Kadell on symmetric and anti-symmetric Macdonald polynomials.
Ivan CherednikDec 7, 1995
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