The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold

The orbits of a real form G of a complex semisimple Lie group GC and those of the complexification KC of its maximal compact subgroup K acting on Z=GC/Q, a homogeneous, algebraic, GC-manifold, are finite. Consequently, there is an open G-orbit. Lower-dimensional orbits are on the boundary of the ope...

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Main Author:	B. Ntatin
Format:	Article
Language:	English
Published:	Hindawi Limited 2019-01-01
Series:	Journal of Mathematics
Online Access:	http://dx.doi.org/10.1155/2019/9105474

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spelling	doaj-565ecf6b043e49b2b592844a353ae8a42020-11-25T01:02:29ZengHindawi LimitedJournal of Mathematics2314-46292314-47852019-01-01201910.1155/2019/91054749105474The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag ManifoldB. Ntatin0Department of Mathematics, Austin Peay State University, Clarksville, TN 37043, USAThe orbits of a real form G of a complex semisimple Lie group GC and those of the complexification KC of its maximal compact subgroup K acting on Z=GC/Q, a homogeneous, algebraic, GC-manifold, are finite. Consequently, there is an open G-orbit. Lower-dimensional orbits are on the boundary of the open orbit with the lowest dimensional one being closed. Induced action on the parameter space of certain compact geometric objects (cycles) related to the manifold in question has been characterized using duality relations between G- and KC-orbits in the case of an open G-orbit and more recently lower-dimensional G-orbits. We show that the parameter space associated with the unique closed G-orbit in Z agrees with that of the other orbits characterized as a certain explicitly defined universal domain.http://dx.doi.org/10.1155/2019/9105474
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	B. Ntatin
spellingShingle	B. Ntatin The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold Journal of Mathematics
author_facet	B. Ntatin
author_sort	B. Ntatin
title	The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
title_short	The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
title_full	The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
title_fullStr	The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
title_full_unstemmed	The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
title_sort	parameter space of orbits of a maximal compact subgroup acting on a flag manifold
publisher	Hindawi Limited
series	Journal of Mathematics
issn	2314-4629 2314-4785
publishDate	2019-01-01
description	The orbits of a real form G of a complex semisimple Lie group GC and those of the complexification KC of its maximal compact subgroup K acting on Z=GC/Q, a homogeneous, algebraic, GC-manifold, are finite. Consequently, there is an open G-orbit. Lower-dimensional orbits are on the boundary of the open orbit with the lowest dimensional one being closed. Induced action on the parameter space of certain compact geometric objects (cycles) related to the manifold in question has been characterized using duality relations between G- and KC-orbits in the case of an open G-orbit and more recently lower-dimensional G-orbits. We show that the parameter space associated with the unique closed G-orbit in Z agrees with that of the other orbits characterized as a certain explicitly defined universal domain.
url	http://dx.doi.org/10.1155/2019/9105474
work_keys_str_mv	AT bntatin theparameterspaceoforbitsofamaximalcompactsubgroupactingonaflagmanifold AT bntatin parameterspaceoforbitsofamaximalcompactsubgroupactingonaflagmanifold
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The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold

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