Title of article :
Dynamical R-matrices for Calogero models Original Research Article
Author/Authors :
Michael Forger، نويسنده , , Axel Winterhalder، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2002
Pages :
48
From page :
523
To page :
570
Abstract :
We present a systematic study of the integrability of the Calogero models, degenerate as well as elliptic, associated with arbitrary (semi-)simple Lie algebras and with symmetric pairs of Lie algebras, where “integrability” is understood to encompass not only the existence of a Lax representation for the equations of motion but also the—more far-reaching—existence of a (dynamical) R-matrix. Using the standard group-theoretical machinery available in this context, we show that integrability of these models, in this sense, can be reduced to the existence of a certain function, denoted here by F, defined on the relevant root system and taking values in the respective Cartan subalgebra, subject to a rather simple set of algebraic constraints: these ensure, in one stroke, the existence of a Lax representation and of a dynamical R-matrix, all given by explicit formulas. We also show that among the simple Lie algebras, only those belonging to the A-series admit a solution of these constraints, whereas the AIII-series of symmetric pairs of Lie algebras, corresponding to the complex Grassmannians SU(p,q)/S(U(p)×U(q)), allows non-trivial solutions when |p−q|⩽1. Apart from reproducing all presently known dynamical R-matrices for Calogero models, our method provides new ones, namely for the degenerate models when |p−q|=1 and for the elliptic models when |p−q|=1 or p=q.
Keywords :
Integrable systems , Dynamical R-matrices , Calogero models
Journal title :
Nuclear Physics B
Serial Year :
2002
Journal title :
Nuclear Physics B
Record number :
883572
Link To Document :
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