The Interacting Fock Space of Haldane's Exclusion Statistics

We prove that Haldane exclusion statistics (ES) can be included in the more general class of standard interacting Fock spaces (IFS). This result provides a standard rule to assign in a consistent way the parameters of the most general exclusion statistics and, through the results of [4], it shows that there is a canonical one-to-one correspondence between these parameters and the families of orthogonal polynomials associated to an arbitrary measure with moments of all orders. Such a correspondence has been discovered in a multiplicity of particular cases (see for example [5], [9]). Thus our result gives a rule to identify immediately the family of orthogonal polynomials associated to a given ES. Moreover it allows to extend the ES in a natural way to infinitely many species and in particular it suggests a standard way to take the thermodynamic limit of these statistics.