LOOP VARIABLES AND THE VIRASORO GROUP

We derive an expression in closed form for the action of a finite elem ent of the Virasoro group on generalized vertex operators. This comple ments earlier results giving an algorithm to compute the action of a f inite string of generators of the Virasoro algebra on generalized vert ex operators. The main new idea is to use a first order formalism to r epresent the infinitesimal group element as a loop variable. To obtain a finite group element it is necessary to thicken the loop to a band of finite thickness. This technique makes the calculation very simple.