W-INFINITY GRAVITY - A GEOMETRIC APPROACH

A brief review is given of an adaptation of the coadjoint orbit method appropriate for the study of models with infinite-dimensional symmetr y groups. It is illustrated on several examples, including derivation of the WZNW action of induced D = 2 (N, 0) supergravity. As the main a pplication, we present the geometric action on a generic coadjoint orb it of the deformed group of area-preserving diffeomorphisms. This acti on is precisely the anomalous effective WZNW action of D = 2 matter fi elds coupled to a chiral W(infinity) gravity background. Similar actio ns are given which produce the KP hierarchy as on-shell equations of m otion.