Abstract: The Kirillov formula is an important formula in representation theory which represents the character of a representation as an integral over a certain orbit of the group in its coadjoint represention. In 80's, this formula was extended as an index formula with infinitesimal group action by Berline-Vergne and Bismut. In this talk, we will extend this formula to the family version. This is a joint work with Xiaonan Ma recently.