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Quantum Algebra papers — page 2

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Theory of linear G-difference equations
We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of…
Per K. Jakobsen, Valentin V. LychaginDec 17, 1997
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Tensor product representations of the quantum double of a compact group
We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations.…
T. H. Koornwinder, F. A. Bais, N. M. MullerDec 17, 1997
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Deformed Harmonic Oscillator Algebras defined by their Bargmann representations
Deformed Harmonic Oscillator Algebras are generated by four operators, two mutually adjoint a and a, and two self-adjoint N and the unity 1 such as: $[a,N] = a, [a, N]=…
M. Irac-Astaud, G. RideauDec 17, 1997
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On some Hochschild cohomology classes of fusion algebras
The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the…
A. A. DavydovDec 16, 1997
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Double Lie algebras and Manin triples
The construction of Lie bialgebra from double Lie algebra is presented. It is used to relate some types of cobracket on inhomogenous so(p,q) algebras with double Lie algebra structures on so(p+1,q)…
P. StachuraDec 15, 1997
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Genus-zero modular functors and intertwining operator algebras
In [H5] (q-alg/9512024) and [H7] (q-alg/9704008), the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving…
Yi-Zhi HuangDec 13, 1997
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Braid group approach to the derivation of universal Ř matrices
A new method for deriving universal Ř matrices from braid group representation is discussed. In this case, universal Ř operators can be defined and expressed in terms of products of braid group…
Feng Pan, Lianrong DaiDec 13, 1997
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Universal Solutions of Quantum Dynamical Yang-Baxter Equations
We construct a universal trigonometric solution of the Gervais-Neveu-Felder equation in the case of finite dimensional simple Lie algebras and finite dimensional contragredient simple Lie…
D. Arnaudon, E. Buffenoir, E. Ragoucy et al.Dec 12, 1997
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The Cremmer-Gervais solution of the Yang-Baxter equation
A direct proof is given of the fact that the Cremmer-Gervais R-matrices satisfy the Yang-Baxter equation.
Timothy J. HodgesDec 12, 1997
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A solution of the quantum Knizhnik Zamolodchikov equation of type Cn
We construct a solution of Cherednik's quantum Knizhnik Zamolodchikov equation associated with the root system of type Cn. This solution is given in terms of a restriction of a…
K. MimachiDec 12, 1997
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Quasi-Hopf twistors for elliptic quantum groups
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda…
M. Jimbo, H. Konno, S. Odake et al.Dec 11, 1997
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Nonstandard solutions of the Yang-Baxter equation
Explicit solutions of the quantum Yang-Baxter equation are given corresponding to the non-unitary solutions of the classical Yang-Baxter equation for sl(5).
Anthony Giaquinto, Timothy J. HodgesDec 11, 1997
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Some Properties of Finite-Dimensional Semisimple Hopf Algebras
Kaplansky conjectured that if H is a finite-dimensional semisimple Hopf algebra over an algebraically closed field k of characteristic 0, then H is of Frobenius type (i.e. if V is an irreducible…
Pavel Etingof, Shlomo GelakiDec 11, 1997
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The Potts Model with a Reflecting Boundary
A Potts model with a reflecting boundary is introduced and it is shown that its partition function can be expressed as a Markov trace on the Temperley-Lieb Algebra of Coxeter type B.
Reinhard Häring-OldenburgDec 11, 1997
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Actions of Tensor Categories and Cylinder Braids
Categorial actions of braided tensor categories are defined and shown to be the right framework for a discussion of the categorial structure related to the group of braids in the cylinder. A Kauffman…
Reinhard H"aring-OldenburgDec 11, 1997
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An Ariki-Koike like extension of the Birman-Murakami-Wenzl Algebra
We introduce an Ariki-Koike like extension of the Birman-Murakami-Wenzl Algebra and show it to be semi-simple. This algebra supports a faithful Markov trace that gives rise to link invariants of…
Reinhard Häring-OldenburgDec 11, 1997
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Two-parameter deformation of loop algebras and superalgebras
We discuss two-parameter deformations of an universal enveloping algebra U(g[u]) of a polynomial loop algebra g[u], where g is a finite-dimensional complex simple Lie algebra (or superalgebra).…
Valeriy N. TolstoyDec 11, 1997
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Positivity of Dunkl's intertwining operator
For a finite reflection group on RN, the associated Dunkl operators are parametrized first-order differential-difference operators which generalize the usual partial derivatives. They generate…
Margit RöslerDec 11, 1997
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Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras
The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(p), where p stands for a set of mutually commuting variables. A family of SL(n)-type solutions of this…
L. K. Hadjiivanov, A. P. Isaev, O. V. Ogievetsky et al.Dec 10, 1997
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The quantum Euler class and the quantum cohomology of the Grassmannians
The Poincare duality of classical cohomology and the extension of this duality to quantum cohomology endows these rings with the structure of a Frobenius algebra. Any such algebra possesses a…
Lowell AbramsDec 9, 1997
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Past the Highest-Weight, and What You Can Find There
The properties of highest-weight representations of the N=2 superconformal algebra in two dimensions can be considerably simplified when re-expressed in terms of relaxed sl(2) representations. This…
A M SemikhatovDec 9, 1997
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Screening Current Representation of Quantum Superalgebras
In this letter a screening current or contour representation is given of certain quantum superalgebras. The Gomez-Sierra construction of quantum groups in conformal field theory is generalized to…
J. RasmussenDec 7, 1997
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τ-function within group theory approach and its quantization
This is a review of the results related to generalizations of the notion of τ-function and integrable hierarchies and to their interpretation within the group theory framework that admits an…
A. MironovDec 7, 1997
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Classification of eight-vertex solutions of the colored Yang-Baxter equation
In this paper all eight-vertex type solutions of the colored Yang-Baxter equation dependent on spectral as well as color parameter are given. It is proved that they are composed of three groups of…
Shi-kun WangDec 5, 1997
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Unification of parastatistics defined as triple operator algebras
We unify parastatistics, defined as triple operator algebras represented on Fock space, in a simple way using the transition number operators. We express them as a normal ordered expansion of…
S. Meljanac, M. Milekovic, M. StojicDec 4, 1997
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