On certain domains in cycle spaces of flag manifolds
type: Item
instance of: scholarly article
title: On certain domains in cycle spaces of flag manifolds
zbMATH Open document ID: 1026.32045
published in: Mathematische Annalen
publication date: 2002-12-01T00:00:00Z
review text: Let \(G^\mathbb{C}/K^\mathbb{C}\) be the affine homogeneous space associated to a real semisimple Lie group \(G\) with maximal compact subgroup \(K\). The author studies some naturally defined \(G\)-invariant neighborhoods of its real points \(M_\mathbb{R}=G/K\). For example, the universal Iwasawa domain \(\Omega_I\) is introduced from the point of view of incidence geometry and some of its properties are obtained: it is Stein, Kobayashi hyperbolic and contains the domain \(\Omega_{AG}\) introduced by Akhiezer and Gindikin. The paper develops some methods to study the Wolf domain \(\Omega_W(D)\) of cycles in an open \(G\)-orbit \(D\) in a flag manifold \(G^\mathbb{C}/P\). The key method is the study of the Schubert domain \(\Omega_S(D)\) which is defined by Schubert cycles of complementary dimension to the cycles.
Mathematics Subject Classification ID: 32M10
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 22E10
zbMATH DE Number: 1837107
zbMATH Keywords: affine homogeneous space
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: flag manifold
zbMATH Keywords: Schubert cycles
author: Alan Huckleberry
reviewed by: Vasile Brînzănescu
MaRDI profile type: Publication
full work available at URL: s002080200326
OpenAlex ID: W2034074598
DOI: 10.1007/S002080200326
description: scientific article; zbMATH DE number 1837107