REPRESENTATION-THEORY OF DEFORMED OSCILLATOR ALGEBRAS

The representation theory of deformed oscillator algebras, defined in terms of an arbitrary function of the number operator N, is developed in terms of the eigenvalues of a Casimir operator C. It is shown that according to the nature of the N spectrum, their unitary irreducible r epresentations may fall into one out of four classes, some of which co ntain bosonic, fermionic or parafermionic Fock-space representations a s special cases. The general theory is illustrated by classifying the unitary irreducible representations of the Arik-Coon, Chaturvedi-Srini vasan, and Tamm-Dancoff oscillator algebras, which may be derived from the boson one by the recursive minimal-deformation procedure of Katri el and Quesne. The effects on non-Fock-space representations of the mi nimal deformation and of the quommutator-commutator transformation, co nsidered in such a procedure, are studied in detail.