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All the possible super-conducting order parameters for the LaOFeAs system areclassified by their transformation under the complete crystal symmetry. Thegeneral forms of the super-conducting gap functions for each class arediscussed. We find that the gap functions in such a multi-band system belong tothree types, full gap, nodal type and finite {}``Fermi arc'' type. Possiblephysical consequences caused by different types of gap functions are alsodiscussed.

Classification of the Super-conducting order parameters under the point group symmetry for a multi-band system: application to LaOFeAs