The algebra of observables for identical particles on a line is formul
ated starting from postulated basic commutation relations. A realizati
on of this algebra in the Calogero model was previously known. New rea
lizations are presented here in terms of differentiation operators and
in terms of SU(N)-invariant observables of the Hermitian matrix model
s. Some particular structure properties of the algebra are briefly dis
cussed. (C) 1998 Elsevier Science B.V. All rights reserved.