Special classes of irreducible representations I

TL;DR

The paper introduces special classes of irreducible group representations called thick and dense, explores their properties, and constructs moduli schemes for these classes, advancing the theoretical framework of representation theory.

Contribution

It defines and studies thick and dense representations, establishing their properties and constructing moduli schemes, thus expanding the understanding of irreducible representations.

Findings

Absolute thickness and denseness are open conditions.

Construction of moduli schemes for absolutely thick and dense representations.

Examples illustrating properties of thick representations.

Abstract

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute denseness are open conditions for representations. Thereby, we can construct the moduli schemes of absolutely thick representations and absolutely dense representations. We also describe several results and several examples on thick representations for developing theory of thick representations.