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A real formof a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold.  A maximal compact subgroupofhas special orbits C which are complex submanifolds in the open orbits of.  These special orbits C are characterized as the closed orbits in Z of the complexification K of.  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 ofby 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 formacting 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 offor all real forms will be given by Abu-Shoga and Huckleberry.

international journal of mathematics and mathematical sciences

Cycle Intersection for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mtext>SO</mml:mtext><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:math>-Flag Domains

Cycle Intersection for SOp,q-Flag Domains