Holonomy representations which are a diagonal direct sum of two faithful representations

TL;DR

This paper investigates holonomy representations that can be decomposed into two faithful sub-representations, focusing on cases where these are isomorphic or dual, and provides classification results in low dimensions.

Contribution

It introduces a detailed analysis of holonomy representations with supplementary faithful sub-representations, especially in isomorphic and dual cases, with classifications in small dimensions.

Findings

Classification of holonomy representations with supplementary faithful sub-representations

Analysis of cases where sub-representations are isomorphic or dual

Results on low-dimensional holonomy representation structures

Abstract

We study holonomy representations admitting a pair of supplementary faithful sub-representations. In particular the cases where the sub-representations are isomorphic respectively dual to each other are treated. In each case we have a closer look at the classification in small dimension.