SU(d)-invariant multidimensional q-oscillators with bosonic degeneracy

Multidimensional two-parameter (q(1),q(2))-oscillators are of two kinds: one is invariant under the (ordinary) Lie group SU(d), whereas the other is invariant under the quantum group SUq(d) where q = q(1)/q(2). It is shown that the q(1) = q(2) limit of both of these two-parameter oscillators coincide and give the q-deformed Newton oscillator which can be derived from the standard quantum harmonic oscillator Newton equation. The bosonic degeneracies of the excited levels of these oscillators are different for q(1) not equal q(2), but coincide in the q(1) = q(2) limit.