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Quantum Algebra papers — page 24

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An Alternative to the Chevalley Description of U[sl(n+1)] and Uq[sl(n+1)]
An alternative to the Chevalley description of Lie algebra sl(n+1), of its universal enveloping algebra U[sl(n+1)] and of its q-deformed analogue Uq[sl(n+1)] in terms of generators, called creation…
Tchavdar D. Palev, Preeti ParasharAug 28, 1996
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The radical of a vertex operator algebra
The radical J(V) of a vertex operator algebra V is defined to be the subspace of V consisting of vectors v such that the zero mode o(v)=0 on V where o(v)=vwt v-1 if v is…
C. Dong, H. Li, G. Mason et al.Aug 26, 1996
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Binomial formula for Macdonald polynomials
We prove a binomial formula for Macdonald polynomials and consider applications of it.
Andrei OkounkovAug 23, 1996
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Shifted Jack polynomials, binomial formula, and applications
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
Andrei Okounkov, Grigori OlshanskiAug 23, 1996
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Bicovariant Differential Calculi and Cross Products on Braided Hopf Algebras
We consider Hopf bimodules and crossed modules over a Hopf algebra H in a braided category. They are the key-stones for braided bicovariant differential calculi and their invariant vector fields…
Yuri Bespalov, Bernhard DrabantAug 23, 1996
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8 Lectures on quantum groups and q-special functions
Lecture notes for an eight hour course on quantum groups and q-special functions at the fourth Summer School in Differential Equations and Related Areas, Universidad Nacional de Colombia and…
Erik KoelinkAug 22, 1996
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Classification of Bicovariant Differential Calculi
We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations V of the quantum group enveloping…
S. MajidAug 21, 1996
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Symmetric Multiplets in Quantum Algebras
We consider a modified version of the coproduct for (q(2)) and show that in the limit when q → 1, there exists an essentially non-cocommutative coproduct. We study the…
L. C. Kwek, C. H. Oh, K. SinghAug 21, 1996
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On the Two q-Analogue Logarithmic Functions
There is a simple, multi-sheet Riemann surface associated with eq(z)'s inverse function lnq(w) for 0< q < 1. A principal sheet for lnq(w) can be defined. However, the topology of the Riemann…
Charles A. Nelson, Michael G. GartleyAug 19, 1996
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Spin Topological Quantum Field Theories
Starting from the quantum group SLq(2,C), we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the…
Anna BeliakovaAug 17, 1996
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A new scalar product for nonsymmetric Jack polynomials
Symmetric Jack polynomials arise naturally in several contexts, including statistics, physics, combinatorics, and representation theory. They are pairwise orthogonal with repsect to two different…
Siddhartha SahiAug 16, 1996
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Dirac operators on quantum SU(2) group and quantum sphere
Definition of Dirac operators on the quantum group SUq(2) and the quantum sphere S2q μ are discussed. In both cases similar SUq(2)-invariant form is obtained. It is connected with…
P. N. Bibikov, P. P. KulishAug 15, 1996
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New rational solutions of Yang-Baxter equation and deformed Yangians
In this paper a class of new quantum groups is presented: deformed Yangians. They arise from rational solutions of the classical Yang-Baxter equation of the form c2 /u + const . The universal…
A. Stolin, P. P. KulishAug 14, 1996
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The Problem of Differential Calculus on Quantum Groups
The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss…
Gustav W. DeliusAug 14, 1996
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Compact automorphism groups of vertex operator algebras
Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary,…
Chongying Dong, Haisheng Li, Geoffrey MasonAug 13, 1996
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Special functions and q-commuting variables
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally…
Tom H. KoornwinderAug 13, 1996
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Ohtsuki's Invariants are of Finite Type
Using a vanishing condition on certain combinations of components of the Jones polynomial for algebraically split links we show that Ohtsuki's invariants of integral homology three spheres are of…
Andrew Kricker, Bill SpenceAug 7, 1996
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Quasi-Hopf algebras associated with sl(2) and complex curves
We construct quasi-Hopf algebras quantizing double extensions of the Manin pairs of Drinfeld, associated to a curve with a meromorphic differential, and the Lie algebra sl(2). This construction makes…
B. Enriquez, V. RubtsovAug 4, 1996
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Fedosov *-products and quantum momentum maps
We study various aspects of Fedosov star-products on symplectic manifolds. By introducing the notion of "quantum exponential maps", we give a criterion characterizing Fedosov connections. As…
Ping XuAug 3, 1996
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Identities in Representations of the Hecke Algebra
New identities on traces of representations of the Hecke algebra on the spaces of paths on graphs are presented. These identities are relevant in the computation of partition functions with fixed…
S. Loesch, Y-K Zhou, J-B ZuberAug 2, 1996
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Generalization and Deformation of Drinfeld quantum affine algebras
Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this paper, we will present a generalization…
Jintai Ding, Kenji IoharaAug 1, 1996
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Zeros and poles of quantum current operators and the condition of quantum integrability
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we study the zeros and poles…
Jintai Ding, Tetsuji MiwaAug 1, 1996
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Drinfeld comultiplication and vertex operators
For the current realization of the quantum affine algebras, Drinfeld gave a simple comultiplication of the quantum current operators. With this comultiplication, we study the related vertex operators…
Jintai Ding, Kenji IoharaAug 1, 1996
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On pentagon, ten-term, and tetrahedron relations
The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of solutions are found. O-doubles of Novikov, which generalize the…
R. M. Kashaev, S. M. SergeevJul 30, 1996
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Level-0 action of Uq(sln) on the q-deformed Fock spaces
On the level-1 Fock space modules of the algebra Uq(sln) we define a level-0 action U0 of the Uq(sln), and an action of an abelian algebra of conserved Hamiltonians commuting…
Kouichi Takemura, Denis UglovJul 30, 1996
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