Classification of Klein Four Symmetric Pairs of Holomorphic Type for $\mathrm{E}_{7(-25)}$

TL;DR

This paper classifies Klein four symmetric pairs of holomorphic type for the Lie group E7(-25) and applies these classifications to derive branching rules.

Contribution

It provides a complete classification of Klein four symmetric pairs of holomorphic type for E7(-25), a task not previously accomplished.

Findings

Classification of Klein four symmetric pairs achieved

Derived branching rules for E7(-25)

Enhanced understanding of symmetric pair structures

Abstract

The author classifies Klein four symmetric pairs of holomorphic type for the non-compact Lie group of Hermitian type $\mathrm{E}_{7(-25)}$, and applies the results to branching rules.