THE MULTIVALUED FREE-FIELD MAPS OF LIOUVILLE AND TODA GRAVITIES

Liouville and Toda gravity theories with non-vanishing interaction pot entials have spectra obtained by dividing the free-field spectra for t hese cases by the Weyl group of the corresponding A(1) or A(2) Lie alg ebra. We study the canonical transformations between interacting and f ree fields using the technique of intertwining operators, giving expli cit constructions for the wavefunctions and showing that they are inva riant under the corresponding Weyl groups. These explicit construction s also permit a detailed analysis of the operator-state maps and of th e nature of the Seiberg bounds.