Cycle Intersection for SOp,q-Flag Domains
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 charac...
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2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/1527973 |
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| author | Faten Abu Shoga |
| author_facet | Faten Abu Shoga |
| author_sort | Faten Abu Shoga |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7ade3e4c16ad458c8a5c3004bc8e5a9d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7ade3e4c16ad458c8a5c3004bc8e5a9d2025-02-03T05:52:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/15279731527973Cycle Intersection for SOp,q-Flag DomainsFaten Abu Shoga0Department of Mathematics, Islamic University of Gaza, P.O. Box 108, Gaza, Gaza Strip, State of PalestineA 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.http://dx.doi.org/10.1155/2020/1527973 |
| spellingShingle | Faten Abu Shoga Cycle Intersection for SOp,q-Flag Domains International Journal of Mathematics and Mathematical Sciences |
| title | Cycle Intersection for SOp,q-Flag Domains |
| title_full | Cycle Intersection for SOp,q-Flag Domains |
| title_fullStr | Cycle Intersection for SOp,q-Flag Domains |
| title_full_unstemmed | Cycle Intersection for SOp,q-Flag Domains |
| title_short | Cycle Intersection for SOp,q-Flag Domains |
| title_sort | cycle intersection for sop q flag domains |
| url | http://dx.doi.org/10.1155/2020/1527973 |
| work_keys_str_mv | AT fatenabushoga cycleintersectionforsopqflagdomains |