  A general algebraic approach, incorporating both invariance groups and
dynamic symmetry algebras, is developed to reveal hidden coherent structures
(closed complexes and configurations) in quantum many-body physics models due
to symmetries of their Hamiltonians $H$. Its general ideas are manifested on
some recent new examples: 1) G-invariant bi-photons and a related
SU(2)-invariant treatment of unpolarized light; 2) quasi-spin clusters in
nonlinear models of quantum optics; 3) construction of composite particles and
(para)fields from G-invariant clusters due to internal symmetries.
