String-inspired gravity coupled to Yang-Mills fields

String-inspired (1+1)-dimensional gravity is coupled to Yang-Mills fields in the Cangemi-Jackiw gauge-theoretical formulation, based on the extended Poincaré group. A family of couplings, which involves metrics obtainable from the physical metric with a conformal rescaling, is considered, and the resulting family of models is investigated both at the classical and at the quantum levels. In particular, also using a series of Kirillov-Kostant phases, the wave functionals that solve the constraints are identified.