# Rigid representations of triangle groups

## TL;DR

This paper generalizes a conjecture about how finite groups of Lie type can be generated, using geometric analysis of representation varieties and tangent spaces.

## Contribution

It introduces a new geometric approach to understanding generation properties of finite groups of Lie type, extending previous conjectures.

## Key findings

- Proves a generalized conjecture on group generation
- Uses geometric properties of representation varieties
- Analyzes tangent spaces to derive results

## Abstract

We prove a generalization of a conjecture of C. Marion on generation properties of finite groups of Lie type, by considering geometric properties of an appropriate representation variety and associated tangent spaces.