Irreducible representations of the group of unipotent matrices of order $4$ over integers

TL;DR

This paper classifies irreducible, finite-weight representations of the unipotent matrix group of order 4 over integers, providing a full description of the moduli space of such representations.

Contribution

It offers a complete classification of pairs of subgroups and characters that produce non-isomorphic irreducible representations, leading to a description of the moduli space.

Findings

Complete classification of subgroup-character pairs

Description of the coarse moduli space

All such representations are monomial

Abstract

We study a coarse moduli space of irreducible representations of the group of unipotent matrices of order $\mathbb{4}$ over the ring of integers which have finite weight. All such representations are known to be monomial. 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.