A remark on Schubert cells and duality of orbits on flag manifolds

2002/08/09 by Simon Gindikin, Toshihiko Matsuki
Mathematics · #math.RT #math.AG #msc:14M15 #msc:32M05

paper · pdf

published as J. Math. Soc. Japan 57(2005), 157--165 · 8 pages

arxiv created 2002/08/09 · arxiv updated 2009/11/30

Abstract

It is known that the closure of an arbitrary K_c-orbit on a flag manifold is expressed as a product of a closed K_c-orbit and a Schubert cell ([M2], [Sp]). We already applied this fact to the duality of orbits on flag manifolds ([GM]). We refine here this result and and give its new applications to the study of domains arising from the duality.

Related

• Cycle spaces of G-orbits in G^\mathbb C-flag manifolds
• The Orbits of the Symplectic Group on the Flag Manifold
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• Experimentation and conjectures in the real Schubert calculus for flag manifolds (extended abstract)
• Schubert slices in the combinatorial geometry of flag domains