  Graphene SU(4) quantum Hall symmetry is extended to SO(8), permitting
analytical solutions for graphene in a magnetic field that break SU(4)
spontaneously. We recover standard graphene SU(4) physics as one limit, but
find new phases and new properties that may be relevant for understanding the
ground state. The graphene SO(8) symmetry is found to be isomorphic to one that
occurs extensively in nuclear structure physics, and very similar to one that
describes high-temperature superconductors, suggesting deep mathematical
connections among these physically-different fermionic systems.
