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Quantum Algebra papers — page 16

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Idempotents of Hecke algebras of type A
We use a skein-theoretic version of the Hecke algebras of type A to present three-dimensional diagrammatic views of Gyoja's idempotent elements, based closely on the corresponding Young diagram. In…
A. K. Aiston, H. R. MortonFeb 12, 1997
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Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case
The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic…
M. A. Semenov-Tian-Shansky, A. V. SevostyanovFeb 11, 1997
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Homological algebra of homotopy algebras
We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads,…
Vladimir HinichFeb 11, 1997
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Higher-Dimensional Algebra III: n-Categories and the Algebra of Opetopes
We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set of…
John C. Baez, James DolanFeb 10, 1997
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Representations of the Lie algebra gl(infinity) and ``reciprocity formula'' for Clebsch-Gordan coefficients
We compare two approaches to the calculation of irreducible characters of the Lie algebra gl(infinity) with negative integral central charge. As a consequence, we obtain a "reciprocity…
Boris ShoikhetFeb 10, 1997
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Matrix elements of vertex operators of deformed W-algebra and Harish Chandra Solutions to Macdonald's difference equations
In this paper we prove that certain matrix elements of vertex operators of deformed W-algebra satisfy Macdonald difference equations and form n! -dimensional space of solutions. These solutions are…
A. Kazarnovski-KrolFeb 8, 1997
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Deformation Theory and the Batalin-Vilkovisky Master Equation
The Batalin-Vilkovisky master equations, both classical and quantum, are precisely the integrability equations for deformations of algebras and differential algebras respectively. This is not a…
Jim StasheffFeb 8, 1997
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Multibraces on the Hochschild complex
We generalize the coupled braces xy of Gerstenhaber and xy,...,z of Getzler depicting compositions of multilinear maps in the Hochschild complex C(A)=Hom(TA;A) of a graded vector space A to…
Fusun AkmanFeb 7, 1997
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The Fundamental Theorem of Vassiliev Invariants
The "fundamental theorem of Vassiliev invariants" says that every weight system can be integrated to a knot invariant. We discuss four different approaches to the proof of this theorem: a…
Dror Bar-Natan, Alexander StoimenowFeb 6, 1997
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A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance
We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of…
G. E. Andrews, A. BerkovichFeb 3, 1997
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Permutation-type solutions to the Yang-Baxter and other n-simplex equations
We study permutation type solutions to n-simplex equations, that is, solutions whose R matrix can be written as a product of delta- functions depending linearly on the indices. With this ansatz the…
Jarmo HietarintaFeb 3, 1997
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q-combinatorics and quantum integrability
The idea that a Dynkin diagram can provide one of the `spatial' variables for an integrable difference-difference system is no news. I propose a `model' where the only variable is of this…
A. Yu. VolkovFeb 3, 1997
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Half-quantum groups at roots of unity, path algebras and representation type
We show that finite dimensional half-quantum groups at roots of unity corresponding to simple Lie algebras having symmetric Cartan matrix are of wild representation type, except for sl2. Moreover,…
Claude CibilsFeb 2, 1997
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Elliptic algebra Aq,p(sl2) in the scaling limit
The scaling limit A,η(sl2) of the elliptic algebra Aq,p(sl2) is investigated. The limiting algebra is defined in terms of a continuous family of generators being Fourier…
S. Khoroshkin, D. Lebedev, S. PakuliakFeb 2, 1997
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q-Deformed Fock spaces and modular representations of spin symmetric groups
We use the Fock space representation of the quantum affine algebra of type A(2)2n to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture…
B. Leclerc, J. -Y. ThibonJan 31, 1997
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On the Witten-Reshetikhin-Turaev representations of mapping class groups
We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to SU(2) and SO(3) induce linear…
Patrick M. GilmerJan 30, 1997
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Kappa-deformed space-time uncertainty relations
We discuss the kappa-deformed phase space obtained as a cross product algebra of the deformed translations algebra and its dual configuration space. We consider two kinds of the kappa-deformed…
Anatol NowickiJan 30, 1997
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Heisenberg Double Description of kappa-Poincare Algebra and kappa-deformed Phase Space
The kappa-deformed dual pair of Poincare algebra and Poincare group is formulated in the framework of Heisenberg doubles. The covariant kappa-deformed phase space is described in detail as a…
J. Lukierski, A. NowickiJan 30, 1997
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Quasitriangular and differential structures on bicrossproduct Hopf algebras
Let X=GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra H=kM k(G) is itself a bicrossproduct kX k(Y)…
E. Beggs, S. MajidJan 30, 1997
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Semi-infinite q-wedge construction of the level 2 Fock Space of Uq(2)
In this proceedings a particular example from KMPY (q-alg/9603025) is presented: the construction of the level 2 Fock space of q(2). The generating ideal of the wedge relations is…
Jens-Ulrik Holger PetersenJan 30, 1997
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A q-analogue of the type A Dunkl operator and integral kernel
We introduce the q-analogue of the type A Dunkl operators, which are a set of degree--lowering operators on the space of polynomials in n variables. This allows the construction of…
T. H. Baker, P. J. ForresterJan 30, 1997
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Quantization of Lie bialgebras, II
This paper is a continuation of "Quantization of Lie bialgebras, I" (q-alg/9606005). We show that the quantization procedure defined in "Quantization of Lie bialgebras, I" is given by…
Pavel Etingof, David KazhdanJan 29, 1997
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Cohomology of Lie superalgebras and of their generalizations
The cohomology groups of Lie superalgebras and, more generally, of color Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is…
M. Scheunert, R. B. ZhangJan 28, 1997
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q-Difference Realization of Uq(sl(M|N)) and Its Application to Free Boson Realization of Uq(sl(2|1))
We present a q-difference realization of the quantum superalgebra Uq(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result we obtain a free boson…
H. Awata, S. Odake, J. ShiraishiJan 28, 1997
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Vertex Operators of Admissible Modules of Uq(C(1)n)
Using our recent bosonic realization of Uq(sp2n), we construct explicitly the vertex operators for the level -1/2 modules of Uq(sp2n) using bosonic fields. Our method…
Naihuan Jing, Yoshitaka KoyamaJan 28, 1997
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