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Quantum Algebra papers — page 25

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A decription of the quantum superalgebra Uq[osp(2n+1/2m)] via Green generators
A description of the orthosymplectic Lie superalgebra osp(2n+1/2m) and also of its q-deformed analogue Uq[osp(2n+1/2m)] in terms of a new set of generators, called Green generators, is given.…
Tchavdar D. PalevJul 29, 1996
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Gauge transformations and quasitriangularity
Natural conditions on a Poisson/quantum group G to implement Poisson/quantum gauge transformations on the lattice are investigated. In addition to our previous result that transformations on one…
S. ZakrzewskiJul 29, 1996
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Examples of categorification
We construct tensor and bitensor categories with given Grothedieck rig (fusion algebra) in simple cases. The results provide examples on which to test the conjectural construction of 4-D TQFT's…
Louis Crane, David N. YetterJul 27, 1996
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Skew Young diagram method in spectral decomposition of integrable lattice models
The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra Uq(sln) is studied. We give a one-to-one…
Anatol N. Kirillov, Atsuo Kuniba, Tomoki NakanishiJul 19, 1996
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A short proof of the integrality of the Macdonald (q,t)-Kostka coefficients
The Macdonald polynomials can be obtained by acting on the constant 1 with creation operators. Three different expressions for these operators are derived, one from the other, in a rather succint…
Luc Lapointe, Luc VinetJul 18, 1996
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Rodrigues formulas for the Macdonald polynomials
We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the…
Luc Lapointe, Luc VinetJul 18, 1996
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Creation operators for the Macdonald and Jack polynomials
Formulas of Rodrigues-type for the Macdonald polynomials are presented. They involve creation operators, certain properties of which are proved and other conjectured. The limiting case of the Jack…
Luc Lapointe, Luc VinetJul 18, 1996
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Anyonic Realization of the Quantum Affine Lie Algebras
We give a realization of the quantum affine Lie algebras and in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter q being…
L. Frappat, A. Sciarrino, S. Sciuto et al.Jul 18, 1996
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Habilitationsschrift: Renormalization and Knot Theory
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to…
Dirk KreimerJul 17, 1996
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Rigidity of K-theory under deformation quantization
Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in…
Jonathan RosenbergJul 16, 1996
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Rogers-Schur-Ramanujan type identities for the M(p,p') minimal models of conformal field theory
We present and prove Rogers-Schur-Ramanujan (Bose/Fermi) type identities for the Virasoro characters of the minimal model M(p,p'). The proof uses the continued fraction decomposition of…
Alexander Berkovich, Barry M. McCoy, Anne SchillingJul 15, 1996
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Formal GNS Construction and States in Deformation Quantization
In this paper we develop a method of constructing Hilbert spaces and the representation of the formal algebra of quantum observables in deformation quantization which is an analog of the well-known…
Martin Bordemann, Stefan WaldmannJul 15, 1996
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K-Theory of Noncommutative Lattices
Noncommutative lattices have been recently used as finite topological approximations in quantum physical models. As a first step in the construction of bundles and characteristic classes over such…
Elisa Ercolessi, Giovanni Landi, Paulo Teotonio-SobrinhoJul 15, 1996
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Noncommutative Lattices and the Algebra of their Continuous Functions
Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of…
Elisa Ercolessi, Giovanni Landi, Paulo Teotonio-SobrinhoJul 15, 1996
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Developing Computer Programs for Knot Classification
In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results…
Charilaos AnezirisJul 15, 1996
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Flag varieties and the Yang-Baxter equation
We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical…
Alain Lascoux, Bernard Leclerc, Jean-Yves ThibonJul 14, 1996
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A Higher-Level Bailey Lemma: Proof and Application
In a recent letter, new representations were proposed for the pair of sequences (γ,δ), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs…
Anne Schilling, S. Ole WarnaarJul 12, 1996
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Associative subalgebras of the Griess algebra and related topics
It is shown how certain idempotents in the Griess algebra generate the discrete series representations for the Virasoro algebra inside the Frenkel-Lepowsky-Meurman's moonshine module vertex…
C. Dong, H. Li, G. Mason et al.Jul 9, 1996
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Differential Calculus on a three-parameter oscillator algebra
Two differential calculi are developped on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same…
M. Irac-AstaudJul 9, 1996
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Demazure Modules and Perfect Crystals
We give a criterion for the Demazure crystal Bw(λ) defined by Kashiwara to have a tensor product structure. We study the symmetric tensor case, and see some Demazure characters are…
Atsuo Kuniba, Kailash C. Misra, Masato Okado et al.Jul 9, 1996
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations
The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan…
H. T. Koelink, J. Van der JeugtJul 9, 1996
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Null-plane Quantum Universal R-matrix
A non-linear map is applied onto the (non-standard) null-plane deformation of (3+1) Poincaré algebra giving rise to a simpler form of this triangular quantization. A universal R-matrix for the null…
A. Ballesteros, F. J. Herranz, C. M. PereñaJul 8, 1996
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Quantization of function algebras on semisimple orbits in *
In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized…
Joseph Donin, Dmitry Gurevich, Steven ShniderJul 8, 1996
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On quantum Jacobi identity
In this paper we present our variant of quantum antisymmetry and quantum Jacobi identity.
Maxim VybornovJul 7, 1996
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Canonical bases and the decomposition matrices of Ariki--Koike algebras
This paper has been withdrawn because of a gap in the proof of Lemma 3.10. The main reults in this paper have now been proved, and extended in the following papers: S. Ariki and A. Mathas, The number…
Andrew MathasJul 5, 1996
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