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Quantum Algebra papers — page 5

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The deformed Virasoro algebra at roots of unity
We discuss some aspects of the representation theory of the deformed Virasoro algebra . In particular, we give a proof of the formula for the Kac determinant and then determine the center of…
P. Bouwknegt, K. PilchOct 22, 1997
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A Burge tree of Virasoro-type polynomial identities
Using a summation formula due to Burge, and a combinatorial identity between partition pairs, we obtain an infinite tree of q-polynomial identities for the Virasoro characters χp, p'r, s,…
Omar Foda, Keith S. M. Lee, Trevor A. WelshOct 21, 1997
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q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
We briefly summarize our systematic construction procedure of q-deforming maps for Lie group covariant Weyl or Clifford algebras.
Gaetano FioreOct 19, 1997
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Effective generalized Seifert-Van Kampen: how to calculate ΩX
Suppose X is a 1-connected simplicial set with finitely many nondegenerate simplices. We give an effective algorithm to calculate a simplicial set with the n-type of the loop space ΩX.…
Carlos SimpsonOct 19, 1997
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Harmonic Analysis on the quantum Lorentz group
This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions…
E. Buffenoir, Ph. RocheOct 17, 1997
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Level one representations of Uq(G2(1))
We construct level one representations of the quantum affine algebra Uq(G2(1)) by vertex operators from bosonic fields.
Naihuan JingOct 17, 1997
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Hecke algebras as subalgebras of Clifford geometric algebras of multivectors
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K2n,B), we proof that theses…
Bertfried FauserOct 16, 1997
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Dirac operator on κ-Minkowski space bicovariant differential calculus and deformed U(1) gauge theory
Derivation of κ-Poincare bicovariant commutation relations between coordinates and 1-forms on κ-Minkowski space is given using Dirac operator and Allain Connes formula. The deformed U(1) gauge…
P. N. BibikovOct 16, 1997
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spl(p,q) superalgebra and differential operators
Series of finite dimensional representations of the superalgebras spl(p,q) can be formulated in terms of linear differential operators acting on a suitable space of polynomials. We sketch the general…
Yves Brihaye, Stefan Giller, Piotr KosinskiOct 14, 1997
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Unitary Representations and BRST Structure of the Quantum Anti--de Sitter Group at Roots of Unity
It is shown that for suitable roots of unity, there exist finite--dimensional unitary representations of Uq(so(2,3)) corresponding to all classical one-particle representations with (half)integer…
Harold SteinackerOct 10, 1997
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Orthogonal Polynomials of Types A and B and Related Calogero Models
Calogero-Sutherland models associated to the Weyl groups of type A and B with exchange terms included in the Hamiltonians systems have non-symmetric eigenfunctions, which are products of the ground…
Charles F. DunklOct 9, 1997
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An Introduction to the Noncommutative Sphere and some Extensions
This is a copy of the talk given at the conference ``Methods in Field Theory'' at Stara Lesna, The Slovak Republic, Sepemeber 22-26, 1997. An introduction to the noncommutative sphere and a…
Jonathan GratusOct 9, 1997
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The zero divisors of the Cayley-Dickson algebras over the real numbers
In this paper we describe algebraically the zero divirsors of the Cayley- Dickson algebras n=2n for n 4 over the real numbers.
R. Guillermo MorenoOct 8, 1997
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Lie Algebras in Fock Space
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
Alexander TurbinerOct 7, 1997
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Braided Deformations of Monoidal Categories and Vassiliev Invariants
Braided deformations of (symmetric) monoidal categories are related to Vassiliev theory by a direct generalization of well-known results relating "quantum" knot invariants to Vassiliev…
David N. YetterOct 6, 1997
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Quantum Orthogonal Cayley-Klein Groups and Algebras
The extension of FRT quantization theory for the nonsemisimple CK groups is suggested. The quantum orthogonal CK groups are realized as the Hopf algebras of the noncommutative functions over an…
N. A. Gromov, I. V. Kostyakov, V. V. KuratovOct 6, 1997
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Quantized Affine Algebras and Crystals with Head
Motivated by the work of Nakayashiki on the inhomogeneous vertex models of 6-vertex type, we introduce the notion of crystals with head. We show that the tensor product of the highest weight crystal…
Seok-Jin Kang, Masaki KashiwaraOct 4, 1997
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Branching functions of An-1(1) and Jantzen-Seitz problem for Ariki-Koike algebras
We study the restrictions of simple modules of Ariki-Koike algebras m() with set of parameters = (ζ;ζv0,... ,ζvl-1), where ζ is an nth root of unity, to their subalgebras…
O. Foda, B. Leclerc, M. Okado et al.Oct 3, 1997
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Vector Fields and Differential Operators: Noncommutative Case
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a…
Andrzej BorowiecOct 2, 1997
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The Algebraic Structure of the gl(n|m) Color Calogero-Sutherland Models
We extend the study on the algebraic structure of the su(n) color Calogero-Sutherland models to the case of gl(n|m) color CS model and show that the generators of the super-Yangian Y(gl(n|m))…
Guo-xing Ju, Shi-kun Wang, Ke WuOct 2, 1997
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A master identity for homotopy Gerstenhaber algebras
We produce a master identity mm=0 for homotopy Gerstenhaber algebras, as defined by Getzler and Jones and utilized by Kimura, Voronov, and Zuckerman in the context of topological conformal field…
Fusun AkmanOct 1, 1997
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Topological Interpretations of Lattice Gauge Field Theory
We construct lattice gauge field theory based on a quantum group on a lattice of dimension 1. Innovations include a coalgebra structure on the connections, and an investigation of connections that…
Doug Bullock, Charles Frohman, Joanna Kania-BartoszyńskaOct 1, 1997
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On shelling and flag vectors
This note defines a flag vector for i-graphs. The construction applies to any finite combinatorial object that can be shelled. Two possible connections to quantum topology are mentioned. Further…
Jonathan FineOct 1, 1997
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Harmonic Oscillator in Characteristic p
We construct an irreducible representation of the canonical commutation relations by operators on a certain Banach space over a local field of characteristic p. The Carlitz polynomials forming the…
Anatoly N. KochubeiOct 1, 1997
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Hochschild cohomology and characteristic classes for star-products
We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham…
Alan Weinstein, Ping XuSep 30, 1997
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