  Electrons in graphene have four flavors associated with low-energy spin and
valley degrees of freedom. The fractional quantum Hall effect in graphene is
dominated by long-range Coulomb interactions which are invariant under
rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at
most filling factors, and also weakly broken by atomic scale valley-dependent
and valley-exchange interactions with coupling constants $g_{z}$ and
$g_{\perp}$. In this paper we demonstrate that when $g_{z}=-g_{\perp}$ an exact
SO(5) symmetry survives which unifies the N\'eel spin order parameter of the
antiferromagnetic state and the $XY$ valley order parameter of the Kekul\'e
distortion state into a single five-component order parameter. The proximity of
the highly insulating quantum Hall state observed in graphene at $\nu=0$ to an
ideal SO(5) symmetric quantum Hall state remains an open experimental question.
We illustrate the physics associated with this SO(5) symmetry by studying the
multiplet structure and collective dynamics of filling factor $\nu=0$ quantum
Hall states based on exact-diagonalization and low-energy effective theory
approaches. This allows to illustrate how manifestations of the SO(5) symmetry
would survive even when it is weakly broken.
