181 research outputs found
A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
We consider the universal solution of the Gervais-Neveu-Felder equation in
the case. We show that it has a quasi-Hopf algebra
interpretation. We also recall its relation to quantum 3-j and 6-j symbols.
Finally, we use this solution to build a q-deformation of the trigonometric
Lam\'e equation.Comment: 9 pages, 4 figure
The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
We quantize the spin Calogero-Moser model in the -matrix formalism. The
quantum -matrix of the model is dynamical. This -matrix has already
appeared in Gervais-Neveu's quantization of Toda field theory and in Felder's
quantization of the Knizhnik-Zamolodchikov-Bernard equation.Comment: Comments and References adde
The R-matrix structure of the Euler-Calogero-Moser model
We construct the -matrix for the generalization of the Calogero-Moser
system introduced by Gibbons and Hermsen. By reduction procedures we obtain the
-matrix for the Euler-Calogero-Moser model and for the standard
Calogero-Moser model.Comment: 7 page
On the Quantum Inverse Problem for the Closed Toda Chain
We reconstruct the canonical operators of the quantum closed Toda
chain in terms of Sklyanin's separated variables.Comment: 16 page
Quantization of Solitons and the Restricted Sine-Gordon Model
We show how to compute form factors, matrix elements of local fields, in the
restricted sine-Gordon model, at the reflectionless points, by quantizing
solitons. We introduce (quantum) separated variables in which the Hamiltonians
are expressed in terms of (quantum) tau-functions. We explicitly describe the
soliton wave functions, and we explain how the restriction is related to an
unusual hermitian structure. We also present a semi-classical analysis which
enlightens the fact that the restricted sine-Gordon model corresponds to an
analytical continuation of the sine-Gordon model, intermediate between
sine-Gordon and KdV.Comment: 29 pages, Latex, minor updatin
Liouville and Toda field theories on Riemann surfaces
We study the Liouville theory on a Riemann surface of genus g by means of
their associated Drinfeld--Sokolov linear systems. We discuss the cohomological
properties of the monodromies of these systems. We identify the space of
solutions of the equations of motion which are single--valued and local and
explicitly represent them in terms of Krichever--Novikov oscillators. Then we
discuss the operator structure of the quantum theory, in particular we
determine the quantum exchange algebras and find the quantum conditions for
univalence and locality. We show that we can extend the above discussion to
Toda theories.Comment: 41 pages, LaTeX, SISSA-ISAS 27/93/E
The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap
The F and B matrices associated with Virasoro null vectors are derived in
closed form by making use of the operator-approach suggested by the Liouville
theory, where the quantum-group symmetry is explicit. It is found that the
entries of the fusing and braiding matrices are not simply equal to
quantum-group symbols, but involve additional coupling constants whose
derivation is one aim of the present work. Our explicit formulae are new, to
our knowledge, in spite of the numerous studies of this problem. The
relationship between the quantum-group-invariant (of IRF type) and
quantum-group-covariant (of vertex type) chiral operator-algebras is fully
clarified, and connected with the transition to the shadow world for
quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce
to the simpler transformation of Babelon and one of the author (J.-L. G.) in a
suitable infinite limit defined by analytic continuation. The above two types
of operators are found to coincide when applied to states with Liouville
momenta going to in a suitable way. The introduction of
quantum-group-covariant operators in the three dimensional picture gives a
generalisation of the quantum-group version of discrete three-dimensional
gravity that includes tetrahedra associated with 3-j symbols and universal
R-matrix elements. Altogether the present work gives the concrete realization
of Moore and Seiberg's scheme that describes the chiral operator-algebra of
two-dimensional gravity and minimal models.Comment: 56 pages, 22 figures. Technical problem only, due to the use of an
old version of uuencode that produces blank characters some times suppressed
by the mailer. Same content
Composition of Kinetic Momenta: The U_q(sl(2)) case
The tensor products of (restricted and unrestricted) finite dimensional
irreducible representations of \uq are considered for a root of unity.
They are decomposed into direct sums of irreducible and/or indecomposable
representations.Comment: 27 pages, harvmac and tables macros needed, minor TeXnical revision
to allow automatic TeXin
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