NEW TOPOLOGICAL THEORIES AND CONJUGACY CLASSES OF THE WEYL GROUP

The problem of interpreting a set of W-algebra constraints constructed in terms of an arbitrarily twisted scalar field as recursion relation s of some topological theory is addressed. In this picture, the models of topological gravity coupled to A, D or E topological matter, corre spond to taking the scalar field twisted by the Coxeter element of the Weyl group. It turns out that not all conjugacy classes of the Weyl g roup lead to models which allow for such an interpretation. For exampl e, it is shown that for the A algebras there are two possible choices for the conjugacy class, giving a new set of theories in addition to t he conventional ones. Furthermore, it is shown how the new series of t heories contains the conventional series as a subsector. A tentative i nterpretation of this new series in terms of intersection theory is pr esented.