695 research outputs found
Deformed Double Yangian Structures
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N))
are defined for any N, extending the previously known case of N=2. They realise
deformed, centrally extended double Yangian structures DY_r(sl(N)). As in the
quantum affine algebras U_q(sl(N)), and quantum elliptic affine algebras
A_qp(sl(N)), these algebras contain subalgebras at critical values of the
central charge c=-N-Mr (M integer, 2r=ln p/ln q), which become Abelian when
c=-N or 2r=Nh for h integer. Poisson structures and quantum exchange relations
are derived for their abstract generators.Comment: 16 pages, LaTeX2e Document - packages amsfonts,amssymb,subeqnarra
Integrable extensions of the rational and trigonometric Calogero Moser potentials
We describe the -matrix structure associated with integrable extensions,
containing both one-body and two-body potentials, of the Calogero-Moser
-body systems. We construct non-linear, finite dimensional Poisson algebras
of observables. Their limit realize the infinite Lie algebras Sdiff in the trigonometric case and
Sdiff in the rational case. It is then isomorphic to the
algebra of observables constructed in the two-dimensional collective string
field theory.Comment: 15 pages; LaTeX; PAR LPTHE 93-23 Revised version including extensive
modifications in the demonstrations and the reference
Explicit solutions of the classical Calogero & Sutherland systems for any root system
Explicit solutions of the classical Calogero (rational with/without harmonic
confining potential) and Sutherland (trigonometric potential) systems is
obtained by diagonalisation of certain matrices of simple time evolution. The
method works for Calogero & Sutherland systems based on any root system. It
generalises the well-known results by Olshanetsky and Perelomov for the A type
root systems. Explicit solutions of the (rational and trigonometric) higher
Hamiltonian flows of the integrable hierarchy can be readily obtained in a
similar way for those based on the classical root systems.Comment: 18 pages, LaTeX, no figur
Classical R-matrix structure for the Calogero model
A classical R-matrix structure is described for the Lax representation of the
integrable n-particle chains of Calogero-Olshanetski-Perelo\-mov. This R-matrix
is dynamical, non antisymmetric and non-invertible. It immediately triggers the
integrability of the Type I, II and III potentials, and the algebraic
structures associated with the Type V potential.Comment: Latex file 9 page
The Classical -Matrix for the Relativistic Ruijsenaars-Schneider System
We compute the classical -matrix for the relativistic generalization of
the Calogero-Moser model, or Ruijsenaars-Schneider model, at all values of the
speed-of-light parameter . We connect it with the non-relativistic
Calogero-Moser -matrix and the
sine-Gordon soliton limit.Comment: LaTeX file, no figures, 8 page
Deformed Virasoro algebras from elliptic quantum algebras
We revisit the construction of deformed Virasoro algebras from elliptic
quantum algebras of vertex type, generalizing the bilinear trace procedure
proposed in the 90's. It allows us to make contact with the vertex operator
techniques that were introduced separately at the same period. As a by-product,
the method pinpoints two critical values of the central charge for which the
center of the algebra is extended, as well as (in the case) a Liouville
formula.Comment: 24 page
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