Generic 1-connectivity of flag domains in Hermitian symmetric spaces

TL;DR

This paper investigates the conditions under which flag domains within certain Hermitian symmetric spaces are generically 1-connected and pseudoconcave, providing a classification in specific types.

Contribution

It determines which pseudoconcave flag domains in irreducible Hermitian symmetric spaces of type AIII or CI are generically 1-connected.

Findings

Identifies conditions for 1-connectedness in flag domains

Classifies pseudoconcave flag domains in specific Hermitian symmetric spaces

Enhances understanding of the geometric structure of flag domains

Abstract

A flag domain is an open real group orbit in a complex flag manifold. It has been shown that a flag domain is either pseudoconvex or pseudoconcave. Moreover, generically 1-connected flag domains are pseudoconcave. In this study, for flag domains contained in irreducible Hermitian symmetric spaces of type AIII or CI, we determine which pseudoconcave flag domain is generically 1-connected.