  We show that the classical non-abelian pure Chern-Simons action is related to
nonrelativistic models in (2+1)-dimensions, via reductions of the gauge
connection in Hermitian symmetric spaces. In such models the matter fields are
coupled to gauge Chern-Simons fields, which are associated with the isotropy
subgroup of the considered symmetric space. Moreover, they can be related to
certain (integrable and non-integrable) evolution systems, as the Ishimori and
the Heisenberg model. The main classical and quantum properties of these
systems are discussed in connection with the topological field theory and the
condensed matter physics.
