Representations of automorphism groups of finite o-modules of rank two

Let o be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite o-module M of rank two. The main emphasis is on the interaction between the different groups and their representations. An induction scheme is developed in order to study the whole family of these groups coherently. The results obtained depend on the ring o in a very weak manner, mainly through the degree of the residue field. In particular, a uniform description of the irreducible representations of GL2(o/pℓ) is obtained, where p is the maximal ideal of o.