Cycle Intersection for SOp,q-Flag Domains
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-03-02
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
A real form G0 of a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold Z=G/Q.
A maximal compact subgroup K0 of G0 has special orbits C which are complex submanifolds in the open orbits of G0.
These special orbits C are characterized as the closed orbits in Z of the complexification K of K0.
These are referred to as cycles.
The cycles intersect Schubert varieties S transversely at finitely many points.
Describing these points and their multiplicities was carried out for all real forms of SLn,ℂ by Brecan (Brecan, 2014) and (Brecan, 2017) and for the other real forms by Abu-Shoga (Abu-Shoga, 2017) and Huckleberry (Abu-Shoga and Huckleberry).
In the present paper, we deal with the real form SOp,q acting on the SO (2n, C)-manifold of maximal isotropic full flags.
We give a precise description of the relevant Schubert varieties in terms of certain subsets of the Weyl group and compute their total number.
Furthermore, we give an explicit description of the points of intersection in terms of flags and their number.
The results in the case of G/Q for all real forms will be given by Abu-Shoga and Huckleberry.
American Psychological Association (APA)
Abu Shoga, Faten. 2020. Cycle Intersection for SOp,q-Flag Domains. International Journal of Mathematics and Mathematical Sciences،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1172601
Modern Language Association (MLA)
Abu Shoga, Faten. Cycle Intersection for SOp,q-Flag Domains. International Journal of Mathematics and Mathematical Sciences No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1172601
American Medical Association (AMA)
Abu Shoga, Faten. Cycle Intersection for SOp,q-Flag Domains. International Journal of Mathematics and Mathematical Sciences. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1172601
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1172601