  Pairing symmetry is important to indentify the pairing mechanism. The
analysis becomes particularly timely and important for the newly discovered
iron-based multi-orbital superconductors. From group theory point of view we
classified all pairing matrices (in the orbital space) that carry irreducible
representations of the system. The quasiparticle gap falls into three
categories: full, nodal and gapless. The nodal-gap states show conventional
Volovik effect even for on-site pairing. The gapless states are odd in orbital
space, have a negative superfluid density and are therefore unstable. In
connection to experiments we proposed possible pairing states and implications
for the pairing mechanism.
