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The mathematical framework for an exact quantization of the two-dimensionalcoset space sigma-models coupled to dilaton gravity, that arise fromdimensional reduction of gravity and supergravity theories, is presented.Extending previous results the two-time Hamiltonian formulation is obtained,which describes the complete phase space of the model in the isomonodromicsector. The Dirac brackets arising from the coset constraints are calculated.Their quantization allows to relate exact solutions of the correspondingWheeler-DeWitt equations to solutions of a modified (Coset)Knizhnik-Zamolodchikov system. On the classical level, a set of observables isidentified, that is complete for essential sectors of the theory. Quantumcounterparts of these observables and their algebraic structure areinvestigated. Their status in alternative quantization procedures is discussed,employing the link with Hamiltonian Chern-Simons theory.Comment: 46 pages, LaTeX2e, 3 figures, revised version to appear in Commun.  Math. Phy

Quantization of Coset Space σ-Models Coupled to Two-Dimensional Gravity