RECIPROCITY LAWS IN THE VERLINDE FORMULAS FOR THE CLASSICAL-GROUPS

The Verlinde formula is computed for each of the simply-connected clas sical Lie groups, and it is shown that the resulting formula obeys cer tain reciprocity laws with respect to the exchange of the rank and the level. Some corresponding dualities between spaces of sections of the ta line bundles over moduli spaces of G-bundles on curves are conjectu red but not proved.