On the Reduced Canonical Quantization of the Induced 2d-gravity

The quantization of the induced 2d-gravity on a compact spatial section is carried out in three different ways. In the three approaches the supermomentum constraint is solved at the classical level but they differ in the way the hamiltonian constraint is imposed. We compare these approaches establishing an isomorphism between the resulting Hilbert spaces. † Work partially supported by the C.I.C.Y.T. and the D.G.I.C.Y.T.