SIMPLE SINGULARITIES AND N=2 SUPERSYMMETRIC YANG-MILLS THEORY

We present a first step towards generalizing the work of Seiberg and W itten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge group s. Specifically, we propose a particular sequence of hyperelliptic gen us n-1 Riemann surfaces to underly the quantum moduli space of SU(n) N =2 supersymmetric gauge theory. These curves have an obvious generaliz ation to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We als o give some remarks on a possible relation to string theory.