  In the dense-neutrino region above the neutrino sphere of a supernova (r >
400 km), neutrino-neutrino refraction causes collective flavor transformations.
They can lead to "spectral splits" where an energy E_split splits the
transformed spectrum sharply into parts of almost pure but different flavors.
Unless there is an ordinary MSW resonance in the dense-neutrino region, E_split
is determined by flavor-lepton number conservation alone. Spectral splits are
created by an adiabatic transition between regions of large and small neutrino
density. We solve the equations of motion in the adiabatic limit explicitly and
provide analytic expressions for a generic example.
