  We review application of the SU(4) model of strongly-correlated electrons to
cuprate and iron-based superconductors. A minimal self-consistent
generalization of BCS theory to incorporate antiferromagnetism on an equal
footing with pairing and strong Coulomb repulsion is found to account
systematically for the major features of high-temperature superconductivity,
with microscopic details of the parent compounds entering only parametrically.
This provides a systematic procedure to separate essential from peripheral,
suggesting that many features exhibited by the high-$T\tsub c$ data set are of
interest in their own right but are not central to the superconducting
mechanism. More generally, we propose that the surprisingly broad range of
conventional and unconventional superconducting and superfluid behavior
observed across many fields of physics results from the systematic appearance
of similar algebraic structures for the emergent effective Hamiltonians, even
though the microscopic Hamiltonians of the corresponding parent states may
differ radically from each other.
