English (United Kingdom)

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

On Representations of General Linear Groups over Principal Ideal Local Rings of Length Two