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Quantum Algebra papers — page 14

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Path integrals and low-dimensional topology
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is…
Boguslaw BrodaMar 19, 1997
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2-Tangles
Just as links may be algebraically described as certain morphisms in the category of tangles, compact surfaces smoothly embedded in R4 may be described as certain 2-morphisms in the 2-category of…
John C. Baez, Laurel LangfordMar 18, 1997
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Non Commutative Differential Geometry, and the Matrix Representations of Generalised Algebras
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the…
Jonathan GratusMar 18, 1997
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Green Function on the q-Symmetric Space SUq(2)/U(1)
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SUq(2), the Green function and the Kernel on the q-homogeneous space M=SU(2)q/U(1) are…
H. Ahmedov, I. H. DuruMar 18, 1997
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Two-parameter Quantum Affine Superalgebra Up,q(gl(1|1)) and Its Drinfeld's Realization
Using super RS construction method and Gauss decomposition, we obtain Drinfeld's currents realization of two-parameter quantum affine superalgebra Up,q(gl(1|1)) and get co-product…
J. F. Cai, S. K. Wang, K. WuMar 17, 1997
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Super Yangian Double DY(gl(1|1)) With Center Extension
We use the super version of RS construction method and Gauss decomposition to obtain Drinfeld's currents realization of super Yangian double DY(gl(1|1)) with center extension
J. F. Cai, G. X. Ju, S. K. Wang et al.Mar 17, 1997
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Super Yangian Double and its Central Extension
We introduce super Yangian double DY[gl(m|n)] and its central extension DY[gl(m|n)]. We give their defining relations in terms of current generators and obtain Drinfeld…
Yao-Zhong ZhangMar 16, 1997
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Certain Topics on the Lie Algebra gl(lambda) Representation Theory
The Lie algebra gl(lambda) dependent on the complex parameter lambda is a continuous version of the Lie algebra gl(inf) of infinite matrices with only finite number of nonzero entries. The gl(lambda)…
B. B. ShoikhetMar 15, 1997
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Finite-dimensional Representations of Quantum Affine Algebras
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the…
Tatsuya Akasaka, Masaki KashiwaraMar 14, 1997
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Wheels, Wheeling, and the Kontsevich Integral of the Unknot
We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a formula (also conjectured independently by Deligne) for the relation between the two natural products…
Dror Bar-Natan, Stavros Garoufalidis, Lev Rozansky et al.Mar 13, 1997
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q-Deformed Schrödinger Equation
We found hermitian realizations of the position vector r, angular momentum Λ and linear momentum p behaving like vectors with respect to the SUq(2) algebra, generated by…
Mircea MicuMar 13, 1997
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The binomial formula for nonsymmetric Macdonald polynomials
Inhomogeneous analogues of symmetric and nonsymmetric Macdonald polynomials were introduced by F. Knop and the author. In the symmetric case A. Okounkov has recently proved a beautiful expansion…
Siddhartha SahiMar 12, 1997
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Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical…
M. A. Semenov-Tian-ShanskyMar 12, 1997
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Drinfel'd Realization of Quantum Affine Superalgebra Uq(gl(1|1))
We obtain Drinfel'd's realization of quantum affine superalgebra Uq(gl(1|1)) based on the super version of RS construction method and Gauss decomposition.
J. F. Cai, S. K. Wang, K. Wu et al.Mar 12, 1997
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Spinon decomposition and Yangian structure of (sln) modules
We review several fermionic-type character formulae for the characters of the integrable highest weight modules of sl(n) at level l=1, and explain how they arise from a spinon basis for these…
Peter Bouwknegt, Kareljan SchoutensMar 12, 1997
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Comments on Drinfeld Realization of Quantum Affine Superalgebra Uq[gl(m|n)(1)] and its Hopf Algebra Structure
By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain Drinfeld current realization for quantum affine superalgebra Uq[gl(m|n)(1)]. We find a…
Yao-Zhong ZhangMar 11, 1997
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Elliptic quantum groups Eτ,η(sl2) and quasi-Hopf algebras
We construct an algebra morphism from the elliptic quantum group Eτ,η(sl2) to a certain elliptic version of the ``quantum groups in higher genus'' studied by V. Rubtsov and the first…
B. Enriquez, G. FelderMar 10, 1997
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Nambu mechanics, n-ary operations and their quantization
We start with an overview of the "generalized Hamiltonian dynamics" introduced in 1973 by Y. Nambu, its motivations, mathematical background and subsequent developments -- all of it on the…
Moshe Flato, Giuseppe Dito, Daniel SternheimerMar 10, 1997
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Modular invariance of trace functions in orbifold theory
The goal of the present paper is to provide a mathematically rigorous foundation to certain aspects of rational orbifold conformal field theory, in other words the theory of rational vertex operator…
Chongying Dong, Haisheng Li, Geoffrey MasonMar 9, 1997
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Traces of creation-annihilation operators and Fredholm's formulas
We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation…
Alexander ChervovMar 9, 1997
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The Dirac operator and gamma matrices for quantum Minkowski spaces
Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal…
P. PodlesMar 6, 1997
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Factorisation of Macdonald polynomials
We discuss the problem of factorisation of the symmetric Macdonald polynomials and present the obtained results for the cases of 2 and 3 variables.
Vadim B. Kuznetsov, Evgueni K. SklyaninMar 6, 1997
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A construction of Hopf algebra cocycles for the double Yangian DY(SL2)
We construct a Hopf algebra cocycle in the Yangian double DY(SL2), conjugating Drinfeld's coproduct to the usual one. To do that, we factorize the twist between two ``opposite''…
B. Enriquez, G. FelderMar 6, 1997
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Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra Uh(sl(2))
Representation theory for the Jordanian quantum algebra U=Uh(sl(2)) is developed. Closed form expressions are given for the action of the generators of U on the basis vectors of finite dimensional…
Joris Van der JeugtMar 6, 1997
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Towards constructing one-particle representations of the deformed Poincaré algebra
We give a method for obtaining states of massive particle representations of the two-parameter deformation of the Poincaré algebra proposed in q-alg/9601010, q-alg/9505030 and q-alg/9501026. We…
I. YakushinMar 5, 1997
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