Exceptional (Z/2Z) x (Z/2Z)-symmetric spaces

TL;DR

This paper classifies (Z/2Z) x (Z/2Z)-symmetric spaces associated with exceptional compact Lie groups and Spin(8), extending previous work and linking to gradings on exceptional Lie algebras.

Contribution

It provides a comprehensive classification of (Z/2Z) x (Z/2Z)-symmetric spaces for exceptional Lie groups, connecting geometric spaces with algebraic gradings.

Findings

Classification of (Z/2Z) x (Z/2Z)-symmetric spaces for exceptional groups

Correspondence with gradings on exceptional Lie algebras

Extension of previous classification results

Abstract

The notion of (Z/2Z) x (Z/2Z)-symmetric spaces is a generalization of classical symmetric spaces, where the group Z/2Z is replaced by (Z/2Z) x (Z/2Z). In this article, a classification is given of the (Z/2Z) x (Z/2Z)-symmetric spaces G/K where G is an exceptional compact Lie group or Spin(8), complementing recent results of Bahturin and Goze. Our results are equivalent to a classification of (Z/2Z) x (Z/2Z)-gradings on the exceptional simple Lie algebras e6, e7, e8, f4, g2 and so(8).