On cycle spaces of flag domains of SLnR

2001 ◽  
Vol 2001 (541) ◽  
Author(s):  
A. T. Huckleberry ◽  
A. Simon ◽  
D. Barlet
Keyword(s):  
Flag Domains

scholarly journals Cycle spaces of infinite dimensional flag domains

2016 ◽  
Vol 50 (4) ◽  
pp. 315-346 ◽  
Author(s):  
Joseph A. Wolf
Keyword(s):  
Infinite Dimensional ◽  
Flag Domains

Poincare Series and Automorphic Cohomology on Flag Domains

1977 ◽  
Vol 105 (3) ◽  
pp. 397 ◽  
Author(s):  
R. O. Wells ◽  
Joseph A. Wolf
Keyword(s):  
Poincaré Series ◽  
Poincare Series ◽  
Flag Domains

Horizontal SL2-orbits in flag domains

1978 ◽  
Vol 235 (1) ◽  
pp. 17-35 ◽  
Author(s):  
Eduardo H. Cattani ◽  
Aroldo G. Kaplan
Keyword(s):  
Flag Domains

Linear cycle spaces in flag domains

2000 ◽  
Vol 316 (3) ◽  
pp. 529-545 ◽  
Author(s):  
Joseph A. Wolf ◽  
Roger Zierau
Keyword(s):  
Flag Domains

Compact Subvarieties in Flag Domains

1994 ◽  
pp. 577-596 ◽  
Author(s):  
Joseph A. Wolf
Keyword(s):  
Flag Domains

Schubert duality for $SL(n,\mathbb{R})$-flag domains

2017 ◽  
Vol 8 (4) ◽  
pp. 553-579
Author(s):  
Ana-Maria Brecan
Keyword(s):  
Flag Domains

scholarly journals Cycle Intersection for SOp,q-Flag Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Faten Abu Shoga
Keyword(s):  
Maximal Compact Subgroup ◽  
Compact Subgroup ◽  
Schubert Varieties ◽  
Real Form ◽  
Precise Description ◽  
Closed Orbits ◽  
Complex Submanifolds ◽  
Complex Semisimple ◽  
Real Forms ◽  
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 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.

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