REPRESENTATION-THEORY OF GENERALIZED DEFORMED OSCILLATOR ALGEBRAS

The representation theory of the generalized deformed oscillator algeb ras (GDOA's) is developed. GDOA's are generated by the four operators {1, a, a(dagger), N}. Their commutators and Hermiticity properties are those of the boson oscillator algebra, except for [a, a(dagger)](q) = G(N), where [a, b](q) = ab - qba and G(N) is a Hermitian, analytic fu nction. The unitary irreductible representations are obtained by means of a Casimir operator C and the semi-positive operator a(dagger)a. Th ey may belong to one out of four classes: bounded from below (BFB), bo unded from above (BFA), finite-dimentional (FD), unbounded (UB). Some examples of these different types of unirreps are given.