# Rigidity of diagonally embedded triangle groups

## TL;DR

This paper proves the local rigidity of certain hyperbolic triangle groups embedded diagonally into higher-dimensional projective and symplectic groups, expanding understanding of their geometric and algebraic properties.

## Contribution

It introduces a new approach to establishing local rigidity of hyperbolic triangle groups via diagonal embeddings into higher-dimensional groups.

## Key findings

- Proves local rigidity of hyperbolic triangle groups in specific embeddings
- Shows these groups are stable under small deformations
- Connects geometric representations with algebraic group embeddings

## Abstract

We show local rigidity of hyperbolic triangle groups generated by reflections in pairs of $n$-dimensional subspaces of $R^{2n}$ obtained by composition of the geometric representation in $PGL(2, R)$ with the diagonal embeddings into $PGL(2n, R)$ and $PSp^\pm(2n, R)$.