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

### Abstract

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.Comment: 21 page

Topics: Mathematics - Representation Theory, 20G25
Year: 2010
DOI identifier: 10.1016/j.jalgebra.2010.05.024
OAI identifier: oai:arXiv.org:1001.5304