Representations and conjugacy classes of general linear groups over principal ideal local rings of length two

2010

Ph.D

HBNI

The irreducible complex representations and conjugacy classes of general linear groups over principal ideal local rings of length two with a fixed finite residue field is studied in this thesis. A canonical correspondence is constructed between the irreducible representations of all such groups which preserves dimensions and a canonical correspondence between the conjugacy classes of all such groups which preserves cardinalities. All the irreducible representations are constructed for general linear groups of order three and four over these rings. It is shown that 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.