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ZEITSCHRIFT FUR PHYSIK C-PARTICLES AND FIELDS, vol.59, no.1, pp.99-103, 1993 (Journal Indexed in SCI)
We discuss the parametrization of quantum groups in terms of independent operators. We find that this consideration leads to the parametrization of SU(q)(2) in terms of a q-oscillator plus a commuting phase. The commuting phase is naturally identified with the subgroup U(1)and the remaining coset SU(q)(2)/U(1)=CP(q)(1) consists of a q-oscillator. For unitary quantum groups SU(q)(n), the analogous construction results in the quantum projective space SU(q)(n + 1)/U(q)(n)=CP(q)(n) being identified with the n-dimensional q-oscillator. This yields a nonlinear action of the quantum group SU(q)(n + 1) on the n-dimensional q-oscillator.