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Quantum Algebra papers — page 29

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Affine Hecke algebras and raising operators for Macdonald polynomials
We introduce certain raising and lowering operators for Macdonald polynomials (of type An-1) by means of Dunkl operators. The raising operators we discuss are a natural q-analogue of raising…
Anatol N. Kirillov, Masatoshi NoumiMay 4, 1996
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The multiple gamma functions and the multiple q-gamma functions
We give an asymptotic expansion (the higher Stirling formula) and an infinite product representation (the Weierstrass product representation) of the Vignéras multiple gamma functions by considering…
Kimio Ueno, Michitomo NishizawaMay 2, 1996
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Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant
We study the asymptotic expansion of the colored Jones polynomial (the Melvin-Morton expansion) using a recursion formula for the deframed universal weight system for the sl(2) Lie algebra.…
Arkady VaintrobMay 2, 1996
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Quasi-Exactly Soluble Potentials and Deformed Oscillators
It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n+1 lowest levels of a given parity can be determined…
Dennis Bonatsos, C. Daskaloyannis, H. A. MavromatisMay 1, 1996
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Differential calculus on `non-standard' (h-deformed) Minkowski spaces
The differential calculus on `non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are…
J. A. de Azcárraga, F. RodenasApr 30, 1996
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Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions
Primary fields of the q-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields…
H. Awata, H. Kubo, Y. Morita et al.Apr 30, 1996
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The algebraic structure of relative twisted vertex operators
Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, ``relativized'' twisted vertex…
Chongying Dong, James LepowskyApr 29, 1996
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Exact two-spinon dynamical correlation function of the Heisenberg model
We derive the exact contribution of two spinons to the dynamical correlation function of the spin-1/2 Heisenberg model. For this, we use the isotropic limits of the exact form factors that have been…
A. H. Bougourzi, M. Couture, M. KacirApr 28, 1996
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On the relation between Uq(sl(2)) vertex operators and q-zonal functions
We show how the states constructed from the action of the modes of bosonized vertex operators, that intertwine Uq(sl(2)) modules, are related to q-zonal functions.
A. H. Bougourzi, L. VinetApr 28, 1996
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Wakimoto construction in the principal gradation
It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra g, with arbitrary level k in the homogeneous gradation, in…
A. H. BougourziApr 28, 1996
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Representation Theory of Lattice Current Algebras
Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum…
A. Yu. Alekseev, L. D. Faddeev, J. Fröhlich et al.Apr 27, 1996
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Knot energies and knot invariants
This an article about some elementary geometric and combinatorial natures of various knot energies. A related "new" knot invariant -- the X-crossing number -- is introduced.
Xiao-Song LinApr 27, 1996
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Jackson Integral Representations of Modified q-Bessel Functions and q-Bessel-Macdonald Functions
The q analog of Modified Bessel functions and Bessel-Macdonald functions, were defined in our previous work (q-alg/950913) as general solutions of a second order difference equations. Here we…
M. A. Olshanetsky, V-B. K. RogovApr 26, 1996
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A Higher-level Bailey Lemma
We propose a generalization of Bailey's lemma, useful for proving q-series identities. As an application, generalizations of Euler's identity, the Rogers-Ramanujan identities, and the…
Anne Schilling, S. Ole WarnaarApr 25, 1996
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Rings of SL2( C)-Characters and the Kauffman Bracket Skein Module
Let M be a compact orientable 3-manifold. The set of characters of SL2( C) representations of the fundamental group of M forms a closed affine algebraic set. We show that its…
Doug BullockApr 20, 1996
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Understanding the Kauffman bracket skein module
The Kauffman bracket skein module K(M) of a 3-manifold M is defined over formal power series in the variable h by letting A=eh/4. For a compact oriented surface F, it is shown that $K(F…
Doug Bullock, Charles Frohman, Joanna Kania-BartoszynskaApr 20, 1996
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Bethe Ansatz for Higher Spin XYZ Models --- Low-lying Excitations ---
A higher spin generalization of the XYZ spin chain defined by the fusion procedure is considered. Energy and momentum of the ground state and low-lying excited states of the model are computed by…
Takashi TakebeApr 19, 1996
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Geometry of q-Hypergeometric Functions as a Bridge between Yangians and Quantum Affine Algebras
The rational quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the Lie algebra sl2 is a system of linear difference equations with values in a tensor product of sl2 Verma…
Vitaly Tarasov, Alexander VarchenkoApr 18, 1996
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Primitive Vassiliev Invariants and Factorization in Chern-Simons Perturbation Theory
The general structure of the perturbative expansion of the vacuum expectation value of a Wilson line operator in Chern-Simons gauge field theory is analyzed. The expansion is organized according to…
M. Alvarez, J. M. F. LabastidaApr 14, 1996
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Geometrical Meaning of R-matrix Action for Quantum Groups at Roots of 1
The present work splits in two parts: first, we perform a straightforward generalization of results from [Re], proving autoquasitriangularity of quantum groups Uq(g) and their…
Fabio GavariniApr 12, 1996
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Universal R-matrix for non-standard quantum sl(2,)
A universal R-matrix for the non-standard (Jordanian) quantum deformation of sl(2,) is presented. A family of solutions of the quantum Yang--Baxter equation is obtained from some finite…
Angel Ballesteros, Francisco J. HerranzApr 11, 1996
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Quantization of Poisson groups -- II
Let Gτ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfeld structure of Poisson group; let Hτ be its dual Poisson group. By means of…
Fabio GavariniApr 10, 1996
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SL(2,C) Topological Quantum Field Theory with Corners
The paper contains the construction of a topological quantum field theory in which gluings along surfaces with boundary are allowed. The construction is made by using quantum deformations of sl(2,C).…
Razvan GelcaApr 10, 1996
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The Universal R-Matrix, Burau Representaion and the Melvin-Morton Expansion of the Colored Jones Polynomial
P. Melvin and H. Morton studied the expansion of the colored Jones polynomial of a knot in powers of q-1 and color. They conjectured an upper bound on the power of color versus the power of q-1. They…
L. RozanskyApr 3, 1996
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Localization of modules over small quantum groups
A report on the works hep-th/9411050, q-alg/9412017, q-alg/9503013, q-alg/9506011 and a joint work with R.Bezrukavnikov.
Michael Finkelberg, Vadim SchechtmanApr 3, 1996
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