20 06 Spin Calogero models and dynamical r - matrices 1

نویسنده

  • L. FEHÉR
چکیده

The main point of the construction of spin Calogero type classical integrable systems based on dynamical r-matrices, developed by L.-C. Li and P. Xu, is reviewed. It is shown that non-Abelian dynamical r-matrices with variables in a reductive Lie algebra F and their Abelian counterparts with variables in a Cartan subalgebra of F lead essentially to the same models.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Class of Integrable Spin Calogero-moser Systems Ii: Exact Solvability

In [LX2], we introduce a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter. Here the main purpose is to give explicit solutions of several factorization problems on infinite dimensional Lie groupoids which will allow us to write down the solutions of these integrable models.

متن کامل

Spin Calogero Particles and Bispectral Solutions of the Matrix Kp Hierarchy

Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r × r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the...

متن کامل

The non-dynamical r-matrices of the degenerate Calogero-Moser models

A complete description of the non-dynamical r-matrices of the degenerate Calogero-Moser models based on gln is presented. First the most general momentum independent r-matrices are given for the standard Lax representation of these systems and those r-matrices whose coordinate dependence can be gauged away are selected. Then the constant r-matrices resulting from gauge transformation are determ...

متن کامل

R-matrices for Elliptic Calogero-Moser Models

The classical R-matrix structure for the n-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independent R-matrix (without spectral parameter) when n ≥ 4. The assumption of momentum independence is sufficient to reproduce the dynamical R-matrices of Avan and Talon for the type I,II,III degenerations of the elliptic potential. The inc...

متن کامل

R-Matrices, Generalized Inverses and Calogero-Moser-Sutherland Models

Four results are given that address the existence, ambiguities and construction of a classical R-matrix given a Lax pair. They enable the uniform construction of R-matrices in terms of any generalized inverse of ad(L). For generic L a generalized inverse (and indeed the Moore-Penrose inverse) is explicitly constructed. The R-matrices are in general momentum dependent and dynamical. We apply our...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006