We study the irreducible complex representations of general linear groups
over principal ideal local rings of length two with a fixed finite residue
field. We construct a canonical correspondence between the irreducible
representations of all such groups which preserves dimensions. For general
linear groups of order three and four over these rings, we construct all the
irreducible representations. We show that the the problem of constructing all
the irreducible representations of all general linear groups over these rings
is not easier than the problem of constructing all the irreducible
representations of the general linear groups over principal ideal local rings
of arbitrary length in the function field case.