The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold
Author
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-01
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Ntatin, B.. 2019. The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold. Journal of Mathematics،Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1181439
Modern Language Association (MLA)
Ntatin, B.. The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold. Journal of Mathematics No. 2019 (2019), pp.1-9.
https://search.emarefa.net/detail/BIM-1181439
American Medical Association (AMA)
Ntatin, B.. The Parameter Space of Orbits of a Maximal Compact Subgroup Acting on a Flag Manifold. Journal of Mathematics. 2019. Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1181439
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1181439