Duality symmetries for N = 2 supersymmetric QCD with vanishing beta-functions

We construct the duality groups for N = 2 supersymmetric QCD with gauge gro up SU(2n + 1) and N-f = 4n + 2 hypermultiplets in the fundamental represent ation. The groups are generated by two elements S and T that satisfy a rela tion (STS-1T)(2n+1) = 1. Thus, the groups are not subgroups of SL(2, Z). We also construct automorphic functions that map the fundamental region of th e group generated by T and STS to the Riemann sphere. These automorphic fun ctions faithfully represent the duality symmetry in the Seiberg-Witten curv e. (C) 1999 Published by Elsevier Science B.V.