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The Multivalued Free-Field Maps of Liouville and Toda Gravities
Liouville and Toda gravity theories with non-vanishing interaction potentials
have spectra obtained by dividing the free-field spectra for these cases by the
Weyl group of the corresponding or Lie algebra. We study the
canonical transformations between interacting and free fields using the
technique of intertwining operators, giving explicit constructions for the
wavefunctions and showing that they are invariant under the corresponding Weyl
groups. These explicit constructions also permit a detailed analysis of the
operator-state maps and of the nature of the Seiberg bounds.Comment: 47 pages, plain Tex, 5 Postscript figures, uses epsf.tex. Repackaging
to permit Postscript generation, no changes to pape