TWISTED SECTOR REPRESENTATIONS OF DISCRETE BACKGROUND SYMMETRIES FOR 2-DIMENSIONAL ORBIFOLDS

We have investigated two-dimensional orbifold compactifications of the closed bosonic string theory subject to modular transformations of the complex background parameter-rho. The representations of the pair of generators s(rho --> 1/rho) and t(rho --> rho-i), which amount to the duality and axionic shift operations respectively, have been determined for the various twisted sectors. This analysis may be performed in two different ways: either by an inspection of correlation functions of twist field ground states on the sphere (Yukawa couplings, etc.), or by deducing the finite symmetry group for fixed values of rho which leaves the correlators of twist fields unaltered. The latter option is closely related to Verlinde's approach providing constraints on the fusion rule algebra. Our results take a form which is familiar from world-sheet modular transformations of characters related to highest weight states in rational conformal field theories.