  Given a Hamiltonian with a continuous symmetry one can generally factorize
that symmetry and consider the dynamics on invariant Hilbert Spaces. In
Statistical Mechanics this procedure is known as the vertex-IRF map, and in
certain cases, like rotational invariant Hamiltonians, can be implemented via
group theoretical techniques. Using this map we translate the DMRG method,
which applies to 1d vertex Hamiltonians, into a formulation adequate to study
IRF Hamiltonians. The advantage of the IRF formulation of the DMRG method ( we
name it IRF-DMRG), is that the dimensions of the Hilbert Spaces involved in
numerical computations are smaller than in the vertex-DMRG, since the
degeneracy due to the symmetry has been eliminated. The IRF-DMRG admits a
natural and geometric formulation in terms of the paths or string algebras used
in Exactly Integrable Systems and Conformal Field Theory. We illustrate the
IRF-DMRG method with the study of the SOS model which corresponds to the spin
1/2 Heisenberg chain and the RSOS models with Coxeter diagram of type A, which
correspond to the quantum group invariant XXZ chain.
