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Quantum Algebra papers — page 21

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Formal GNS Construction and WKB Expansion in Deformation Quantization
In this contribution we review the formal GNS construction developped in a previous preprint (q-alg/9607019), and formulate the usual WKB-expansion in flat 2n-dimensional phase space in terms of a…
M. Bordemann, S. WaldmannNov 4, 1996
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Topics in hidden symmetries. III
This short paper being devoted to some aspects of the inverse problem of the representation theory treats several themes, which have their origins in the researches of F.A.Berezin, D.P.Zhelobenko,…
Denis V. JurievNov 4, 1996
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Singular R-matrices and Drinfeld's comultiplication
We compute the R-matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for Uq(sl2). This R-matrix contains terms proportional to the…
Rinat KedemNov 3, 1996
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Twisted Quantum Affine Algebras
We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.
Vyjayanthi Chari, Andrew PressleyNov 1, 1996
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On Drinfeld realization of quantum affine algebras
We provide a direct proof of the Drinfeld realization for the quantum affine algebras.
Naihuan JingOct 31, 1996
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Quantum Grothendieck polynomials
We study the algebraic aspects of (small) quantum equivariant K-theory of flag manifold. Lascoux-Schützenberger's type formula for quantum double and quantum double dual Grothendieck…
Anatol N. KirillovOct 30, 1996
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Iwahori-Hecke algebras of type A at roots of unity
In this paper, we explore the use of path idempotents for the Hecke algebra of type A at roots of unity. For q a primitive -th root of unity we obain a non-unital imbedding of (a quotient…
Frederick M. Goodman, Hans WenzlOct 28, 1996
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Capelli identities for Lie superalgebras
We apply the technique of affine Hecke algebras to the invariant theory of the "queer" Lie superalgebra qN. We give explicit formulas for the elements of a distinguished basis in the…
Maxim NazarovOct 27, 1996
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On Uh(sl(2)), Uh(e(3)) and their Representations
By solving a set of recursion relations for the matrix elements of the Uh(sl(2)) generators, the finite dimensional highest weight representations of the algebra were obtained as factor…
B. Abdesselam, A. Chakrabarti, R. ChakrabartiOct 25, 1996
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Quantization of Lie bialgebras, III
In this paper we construct explicitly the quantization of Lie bialgebras of -valued functions on a punctured rational or elliptic curve, where is a finite dimensional simple Lie algebra. by…
Pavel Etingof, David KazhdanOct 24, 1996
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Integrality of the Averaged Jones Polynomial of Algebraically Split Links
X.-S. Lin and Z. Wang recently made a conjecture concerning the integrality of the Taylor coefficients of the averaged Jones polynomial of algebraically split links. This question is related to a…
H. U. BodenOct 24, 1996
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Invariants of fibred knots from moduli
An invariant μα(K) of fibred knots K in a homology sphere is defined for each α∈ S Un as follows. Since the knot is fibred, the knot complement is described by an element of…
H. U. BodenOct 24, 1996
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Representations of Uh(su(N)) derived from quantum flag manifolds
A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a…
P. Stovicek, R. TwarockOct 24, 1996
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Topics in hidden symmetries. II
This short paper being devoted to some aspects of the inverse problem of the representation theory briefly treats the interrelations between the author's approach to the setting free of hidden…
Denis V. JurievOct 23, 1996
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Non integrable representations of the restricted quantum analogue of sl(3) at roots of 1
The structure of irreducible representations of (restricted) Uq(sl(3)) at roots of unity is understood within the Gelfand--Zetlin basis. The latter needs a weakened definition for non integrable…
Daniel ArnaudonOct 22, 1996
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Algebraic integrability of the two-body Ruijsenaars operator
We study the algebra of difference operators that commute with the two-body Ruijsenaars operator, a q-deformation of the Lamé differential operator, for generic values of the deformation parameter.…
Giovanni Felder, Alexander VarchenkoOct 18, 1996
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Difference equations of quantum current operators and quantum parafermion construction
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 prove that, for the…
Jintai Ding, Boris FeiginOct 18, 1996
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Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula
We study the algebraic aspects of equivariant quantum cohomology algebra of the flag manifold. We introduce and study the quantum double Schubert polynomials, which are the Lascoux-Schutzenberger…
Anatol N. Kirillov, Toshiaki MaenoOct 17, 1996
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The Twisted Heisenberg Algebra Uh,w( H(4))
A two parametric deformation of the enveloping Heisenberg algebra H(4) which appear as a combination of the standard and a nonstandard quantization given by Ballesteros and Herranz is…
Boucif AbdesselamOct 16, 1996
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Semiinfinite cohomology of quantum groups II
It is known that the semi-infinite cohomology spaces of the infinitely twisted nilpotent subalgebra in an affine Lie algebra g with coefficients in an integrable simple module over the affine Lie…
Sergey ArkhipovOct 15, 1996
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The infinitesimal form of induced representation of the kappa-Poincare group
The infinitesimal form of the induced representation of the kappa-Poincare group is constructed. The infinitesimal action of the kappa-Poincare group on the kappa-Minkowski space is described. The…
Karol PrzanowskiOct 15, 1996
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A new derivation of the inner product formula for the Macdonald symmetric polynomials
We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type An-1. As a special case, the corresponding constant term conjecture is also proved.
Katsuhisa MimachiOct 15, 1996
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Difference equations and symmetric polynomials defined by their zeros
In this paper, we introduce a new family of symmetric polynomials which depends on a parameter r. They are defined by specifying certain of their zeros. For the parameter values 1/2, 1, and 2 they…
Friedrich Knop, Siddhartha SahiOct 15, 1996
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A recursion and a combinatorial formula for Jack polynomials
Heckman and Opdam introduced a non-symmetric analogue of Jack polynomials using Cherednik operators. In this paper, we derive a simple recursion formula for these polynomials and formulas relating…
Friedrich Knop, Siddhartha SahiOct 15, 1996
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Turaev-Viro Modules of Satellite knots
Given an oriented knot K in S3 and a TQFT, Turaev and Viro defined modules somewhat analogous to the Alexander module. We work with the (Vp,Zp) theories of Blanchet, Habegger, Masbaum and Vogel…
Patrick M. GilmerOct 11, 1996
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