Matrix model dualities from conformal field theory

Using the large-N conformal invariant collective field formulation, of the dual matrix model, a strong-weak coupling duality is displayed in terms of the generators of the conformal group. In the large-N limit, the real-symmetric matrix model is dual to the quaternionic-real matrix model and the hermitian matrix model is self-dual. We construct the master Hamiltonian for dual real-symmetric and quaternionic-real matrices and discuss a connection with the hermitian matrix model.