2022•arXiv (Cornell University)Open access

Generic 1-connectivity of flag domains in Hermitian symmetric spaces

Tatsuki Hayama

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.

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Key concepts: Flag (linear algebra), Generalized flag variety, Hermitian symmetric space, Mathematics, Domain (mathematical analysis), Orbit (dynamics), Hermitian matrix, Pure mathematics