Irreducible Representations of the Group of Unipotent Matrices of Order 4 over Integers

Abstract

We study a coarse moduli space of irreducible representations of the group of unipotent matrices of order 4 over the ring of integers that have finite weight. All such representations are known to be monomial (see [4]). To describe a coarse moduli space of such representations, we need to study pairs of subgroups and their characters, which induce non-isomorphic irreducible representations. We obtain a full classification of such pairs and, respectively, a coarse moduli space.