Dynamics of D-branes on SU(2)/U(1) gauged WZW model are investigated. We fi
nd the effective action for infinite k, where k is the level of WZW model.
We also consider finite k correction to the effective action which is compa
tible with Fedosov's deformation quantization of the background. (C) 2001 E
lsevier Science B.V. All rights reserved.