OBSERVABLE ALGEBRAS FOR THE RATIONAL AND TRIGONOMETRIC EULER-CALOGERO-MOSER MODELS

We construct polynomial Poisson algebras of observables for the classi cal Euler-Calogero-Moser (ECM) models. Their structure connects them t o flavour-indexed non-linear W-infinity algebras, albeit with qualitat ive differences. The conserved Hamiltonians and symmetry algebras deri ved in a previous work are subsets of these algebra. We define their l inear, N --> infinity limits, realizing W-infinity type algebras coupl ed to current algebras.