Unified $(p,q;\alpha ,\beta ,\nu ;\gamma )-$deformed oscillator algebra: irreducible representations and induced deformed harmonic oscillator

A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally, the discrete spectrum of the corresponding deformed harmonic oscillator Hamiltonian is investigated and discussed.