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Quantum Algebra papers — page 36

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Isotopic pairs and their representations. II. A general supercase
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are…
Denis V. JurievNov 18, 1995
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Modular functor and representation theory of sl2 at a rational level
We define a new modular functor based on Kac-Wakimoto admissible representations and the corresponding D-module on the moduli space of rank 2 vector bundles with parabolic structure. A new fusion…
B. Feigin. F. MalikovNov 18, 1995
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A gauge-field approach to 3- and 4-manifold invariants
The paper contains a talk given by the author at the Banach Center in Spring 1995. It recapitulates author's approach to construction of topological invariants of the Reshetikhin-Turaev-Witten…
Boguslaw BrodaNov 17, 1995
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h-deformation of GL(1|1)
h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GLq (1|1). The deformation parameter h is odd (grassmann). Related differential calculus…
Ludwik Dabrowski, Preeti ParasharNov 16, 1995
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Cycle for integration for zonal spherical function of type An
Integral of a certain multivalued form over cycle Δ provides zonal spherical function of type An. This paper is devoted to quantum group analysis and verification of monodromy properties of…
A. Kazarnovski-KrolNov 14, 1995
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Intertwining Operators And Quantum Homogeneous Spaces
In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum…
Leonid L. VaksmanNov 13, 1995
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Twisted Yang-Baxter equations for linear quantum (super)groups
We consider the modified (or twisted) Yang-Baxter equations for the SLq(N) groups and SLq(N|M) supergroups. The general solutions for these equations are presented in the case of the linear…
A. P. IsaevNov 13, 1995
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Deformation of Yangian Y(sl2)
A quantization of a non-standard rational solution of CYBE for sl2 is given explicitly. We obtain the quantization with the help of a twisting of the usual Yangian Y(sl2. This quantum object…
S. M. Khoroshkin, A. A. Stolin, V. N. TolstoyNov 10, 1995
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Gauss Decomposition for Quantum Groups and Duality
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation…
E. V. Damaskinski, P. P. Kulish, V. V. Lyakhovsky et al.Nov 10, 1995
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Deformations of the KdV hierarchy and related soliton equations
We define hierarchies of differential--q-difference equations, which are q-deformations of the equations of the generalized KdV hierarchies. We show that these hierarchies are bihamiltonian, one of…
Edward FrenkelNov 6, 1995
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Phase spaces related to standard classical r-matrices
Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly…
S. ZakrzewskiNov 2, 1995
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Double-Bosonisation and the Construction of Uq(g)
We introduce a quasitriangular Hopf algebra or `quantum group' U(B), the double-bosonisation, associated to every braided group B in the category of H-modules over a quasitriangular…
S. MajidNov 2, 1995
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Kac-Peterson, Perron-Frobenius, and the Classification of Conformal Field Theories
The classification of CFTs has an important subproblem, namely classifiying the partition functions for WZW theories. This subproblem is intimately connected to the modular behaviour of the…
Terry GannonOct 30, 1995
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Differential Calculi on the Quantum Group SUq(2) and Global U(1)-covariance
A variety of three-dimensional left-covariant differential calculi on the quantum group SUq(2) is considered using an approach based on global U(1) -covariance. Explicit representations of…
D. G. PakOct 26, 1995
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Nonsemisimple Quantum Groups as Hopf Algebras of the Dual Functions
The nonsemisimple quantum Cayley-Klein groups Fun(SUq(2; j) are realized as Hopf algebra of the noncommutative functions with the dual (or Study) variables. The dual quantum algebras…
N. A. GromovOct 22, 1995
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Connection Between q-Deformed Anharmonic Oscillators and Quasi-Exactly Soluble Potentials
It is proved that quasi-exactly soluble potentials (QESPs) corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n+1 lowest levels of a given parity can be…
Dennis Bonatsos, C. Daskaloyannis, Harry A. MavromatisOct 21, 1995
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The Use of Quantum Groups in Nuclear Structure Problems
Various applications of quantum algebraic techniques in nuclear structure physics, such as the suq(2) rotator model and its extensions, the use of deformed bosons in the description of pairing…
Dennis Bonatsos, C. Daskaloyannis, P. Kolokotronis et al.Oct 21, 1995
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Geometry of the Quantum Complex Projective Space CPq(N)
The quantum deformation CPq(N) of complex projective space is discussed. Many of the features present in the case of the quantum sphere can be extended. The differential and integral calculus is…
Chong-Sun Chu, Pei-Ming Ho, Bruno ZuminoOct 21, 1995
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Quantization of Poisson algebraic groups and Poisson homogeneous spaces
This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers…
Pavel Etingof, David KazhdanOct 20, 1995
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Solutions of Klein--Gordon and Dirac equations on quantum Minkowski spaces
Covariant differential calculi and exterior algebras on quantum homogeneous spaces endowed with the action of inhomogeneous quantum groups are classified. In the case of quantum Minkowski spaces they…
P. PodlesOct 20, 1995
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Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
Coquasitriangular universal R matrices on quantum Lorentz and quantum Poincaré groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10].…
P. PodlesOct 20, 1995
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Representation of SUq(2)-covariant q-Lie Algebra in Terms of Differential Operators
A three-dimensional q-Lie algebra of SUq(2) is realized in terms of first- and second-order differential operators. Starting from the q-Lie algebra one has constructed a left-covariant…
D. G. PakOct 19, 1995
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The Alexander- and Jones-invariants and the Burau module
From the braid-valued Burau module over the braid group we construct the Yang-Baxter matrices yielding the Alexander- and the Jones knot invariants. This generalises an observation of V. F. R. Jones.
Florin Constantinescu, Mirko LueddeOct 17, 1995
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Generalised Magnus modules over the braid group
W.~Magnus' representations of submonoids E ≤ End(F) of the endomorphisms of a free group F of finite rank are generalised by identifying them with the first homology group of F …
Mirko LueddeOct 17, 1995
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Spinor Representations of Uq( gl(n)) and Quantum Boson-Fermion Correspondence
This is an extension of quantum spinor construction in DF2. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum…
Jintai DingOct 17, 1995
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