Symmetry in 2-dimensional gravity

We study the symmetry of 2-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov action by reducing to the conformal or light-cone gauges respectively. The theory is also solved classically. We show that an SL(2,R) covariant gauge can be chosen such that the 2-dimensional gravity has manifest Virasoro and sl(2,R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and αo=1. We give a simple interpretation of these conditions. (author). 31 refs