Classification of reductive real spherical pairs I. The simple case

TL;DR

This paper classifies pairs of simple real Lie algebras and their reductive subalgebras where the entire algebra can be expressed as a sum of the subalgebra and a minimal parabolic subalgebra, focusing on the simple case.

Contribution

It provides a complete classification of reductive real spherical pairs for simple Lie algebras in the minimal parabolic sum context.

Findings

Classification of all such pairs for simple real Lie algebras

Identification of conditions for the existence of minimal parabolic subalgebras

Extension of previous classifications to the simple case

Abstract

This paper gives a classification of all pairs $(\mathfrak g, \mathfrak h)$ with $\mathfrak g$ a simple real Lie algebra and $\mathfrak h < \mathfrak g$ a reductive subalgebra for which there exists a minimal parabolic subalgebra $\mathfrak p < \mathfrak g$ such that $\mathfrak g = \mathfrak h + \mathfrak p$ as vector sum.