# Pseudo-Riemannian almost quaternionic homogeneous spaces with irreducible isotropy

## TL;DR

This paper classifies certain pseudo-Riemannian almost quaternionic homogeneous spaces, showing they are mostly symmetric spaces with some exceptions in lower dimensions, advancing understanding of quaternionic geometry.

## Contribution

It proves that such spaces are locally isometric to quaternionic Kähler symmetric spaces in higher dimensions, and provides a counterexample in dimension 12.

## Key findings

- Spaces of dimension ≥16 are symmetric quaternionic Kähler spaces.
- In dimension 12, a non-symmetric example exists.
- Classification results for pseudo-Riemannian almost quaternionic homogeneous spaces.

## Abstract

We show that pseudo-Riemannian almost quaternionic homogeneous spaces with index 4 and an H-irreducible isotropy group are locally isometric to a pseudo-Riemannian quaternionic K\"ahler symmetric space if the dimension is at least 16. In dimension 12 we give a non-symmetric example.