Classification of Klein Four Symmetric Pairs of Holomorphic Type for $\mathrm{E}_{6(-14)}$

TL;DR

This paper classifies Klein four symmetric pairs of holomorphic type for the non-compact Lie group E_{6(-14)}, identifying pairs of groups where certain irreducible unitary representations remain admissible upon restriction.

Contribution

It provides a comprehensive classification of Klein four symmetric pairs of holomorphic type for E_{6(-14)}, expanding understanding of representation restrictions in this context.

Findings

Identified all Klein four symmetric pairs of holomorphic type for E_{6(-14)}

Established conditions for irreducible unitary representations to be admissible upon restriction

Enhanced the framework for analyzing representations of non-compact Lie groups

Abstract

The author classifies Klein four symmetric pairs of holomorphic type for non-compact Lie group $\mathrm{E}_{6(-14)}$, which gives a class of pairs $(G,G')$ of real reductive Lie group $G$ and its reductive subgroup $G'$ such that there exist irreducible unitary representations $\pi$ of $G$, which are admissible upon restriction to $G'$.