On the number operators of multimode systems of deformed oscillators covariant under quantum groups

For multimode systems of deformed oscillators covariant under the actions of the quantum groups SUq(n), SUq(n mod m), GLp,q(n) and GLp,q(n mod m) the number operators are constructed explicitly in terms of the creation and annihilation operators. The relation between the various kinds of deformed oscillator systems, representations of these oscillator algebras in terms of coordinates and deformed derivatives, realizations of classical groups in non-commutative spaces, and some aspects of the physical behaviour of quantum group covariant oscillator systems are also discussed.