Stereographic variables for multidimensional quantum group covariant q-oscillators

In this paper, we study the unitary matrix representation of quantum group SUq(2) in terms of stereographic coordinates z and z* and a central unitary phase u. The fractional linear transformation of z and z(*) gives the acti on of SUq(2) on the quantum sphere SUq(2)/U(1) with coordinates z and z*. W e then extend this action to SUq(2) and derive the transformation law of u. Finally, we construct the two-dimensional covariant q-oscillators in terms of stereographic variables and then we generalize it to d-dimensional case . (C) 2001 American Institute of Physics.