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Quantum Algebra papers — page 22

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A reproducing kernel for nonsymmetric Macdonald polynomials
We present a new formula of Cauchy type for the nonsymmetric Macdonald polynomials which are joint eigenfunctions of q-Dunkl operators. This gives the explicit formula for a reproducing kernel on the…
K. Mimachi, M. NoumiOct 11, 1996
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Coset construction for winding subalgebras and applications
In this paper we review the coset construction for winding subalgebras of affine Lie algebras. We classify all cosets of central charge c<1 and calculate their branching rules. The…
Peter BouwknegtOct 10, 1996
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On the Drinfeld Twist for Quantum sl(2)
An isomorphism, up to a twist, between the quasitriangular quantum enveloping algebra Uh(sl(2)) and the (classical) U(sl(2))[[h]]is discussed. The universal twisting element F is given up to…
L. Dabrowski, F. Nesti, P. SiniscalcoOct 9, 1996
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Quantum Dynamical R-matrices and Quantum Frobenius Group
We propose an algebraic scheme for quantizing the rational Ruijsenaars-Schneider model in the R-matrix formalism. We introduce a special parameterization of the cotangent bundle over GL(N,C). In new…
G. E. Arutyunov, S. A. FrolovOct 8, 1996
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Quantum Orthogonal Cayley-Klein Groups in Cartesian Basis
The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the…
N. A. Gromov, I. V. Kostyakov, V. V. KuratovOct 8, 1996
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The Quantum Symplectic Cayley-Klein Groups
The contraction method applied to the construction of the nonsemisimple quantum symplectic Cayley-Klein groups Fun(Spq(n;j)) . This groups has been realised as Hopf algebra of the noncommutative…
N. A. Gromov, I. V. Kostyakov, V. V. KuratovOct 8, 1996
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The Polar Decomposition of q-Deformed Boson Algebra
In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity.
W-S. ChungOct 7, 1996
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Deforming Maps for Lie Group Covariant Creation and Annihilation Operators
Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie…
Gaetano FioreOct 4, 1996
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Quantum Heisenberg--Weyl Algebras
All Lie bialgebra structures on the Heisenberg--Weyl algebra [A+,A-]=M are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new…
Angel Ballesteros, Francisco J. Herranz, Preeti ParasharOct 4, 1996
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Induced representations of the one dimensional quantum Galilei group
We study the representations of the quantum Galilei group by a suitable generalization of the Kirillov method on spaces of non commutative functions. On these spaces we determine a quasi-invariant…
F. Bonechi, R. Giachetti, E. Sorace et al.Oct 3, 1996
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New Quantum Groups by Double-Bosonisation
We obtain new family of quasitriangular Hopf algebras C0|nq Uq(sun) C0|nq via the author's recent double-bosonisation construction for new quantum groups.…
S. MajidOct 2, 1996
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Advances in Quantum and Braided Geometry
We demonstrate our recent general results on the Casimir construction and moduli space of all bicovariant calculi by means of some detailed examples, including finite-difference and 2-jet cacluli on…
S. MajidOct 2, 1996
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Irreducible representations of deformed oscillator algebra and q-special functions
Different generators of a deformed oscillator algebra give rise to one-parameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the…
E. V. Damaskinsky, P. P. KulishOct 1, 1996
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Some Realization of glq(n)-covariant Oscillator Algebra and glq(n)-covariant q-Virasoro Algebra with q a root of unity
In this paper some realization of glq(n)-covariant oscillators is obtained when q is a root of unity. And the glq(n)-covariant q-Virasoro algebra is presented by using the glq(n)-covariant…
W-S. ChungOct 1, 1996
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Anyonic Realization of the Quantum Affine Lie Superalgebra Uq(A(M,N)(1))
We give a realization of the quantum affine Lie superalgebras Uq(A(M,N))(1) in terms of anyons defined on a one or two-dimensional lattice, the deformation parameter q being related to the…
L. Frappat, A. Sciarrino, S. Sciuto et al.Sep 30, 1996
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Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement
Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri type…
Jan F. van DiejenSep 30, 1996
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Quantum Affine Algebras at Roots of Unity
We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several new…
Vyjayanthi Chari, Andrew PressleySep 27, 1996
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Paragrassmann Integral, Discrete Systems and Quantum Groups
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition…
A. P. IsaevSep 25, 1996
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Nonstandard quantum groups associated to Belavin-Drinfeld triples
A construction is given of a family of non-standard quantizations of the algebra of functions on a connected complex semi-simple algebraic group. For each ``disjoint'' triple in the sense of…
Timothy J. HodgesSep 23, 1996
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A q-oscillator Green Function
By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.
H. Ahmedov, I. H. DuruSep 23, 1996
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Finite type 3-manifold invariants and the structure of the Torelli
We apply the theory of finite-type invariants of homology 3-spheres to investigate the structure of the Torelli group. We construct natural cocycles in the Torelli group and show that the lower…
Stavros Garoufalidis, Jerome LevineSep 22, 1996
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Coherent States of glq(2)-covariant Oscillators
In this paper two types of coherent states of glq(2)-covariant oscillators are investigated.
W-S. ChungSep 21, 1996
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Skein Quantization and Lattice Gauge Field Theory
This is a survey article describing the various ways in which the Kauffman bracket skein module is a quantization of surface group characters. These include a purely heuristic sense of deformation of…
Doug Bullock, Charles Frohman, Joanna Kania-BartoszynskaSep 21, 1996
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q-deformed Star Products and Moyal Brackets
The standard and anti-standard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called W∞. q-star products and q-Moyal brackets…
O. F. DayiSep 20, 1996
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On Clifford representation of Hopf algebras and Fierz identities
We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from…
Suemi Rodriguez-RomoSep 20, 1996
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