Primitive irreducible representations of finitely generated nilpotent groups

TL;DR

This paper proves that all irreducible representations of finitely generated nilpotent groups over characteristic zero fields are induced from primitive representations of subgroups, providing a structural insight into their representation theory.

Contribution

It establishes that every irreducible representation of such groups can be obtained via induction from primitive subgroup representations, a novel structural result.

Findings

All irreducible representations are induced from primitive subgroup representations.

The result applies to finitely generated nilpotent groups over characteristic zero fields.

Provides a new understanding of the representation structure of nilpotent groups.

Abstract

In the paper we show that any irreducible representation of a finitely generated nilpotent group $G$ over a finitely generated field $F$ of characteristic zero is induced from a primitive representation of some subgroup of $G$.