## Journal of the Mathematical Society of Japan

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

#### Abstract

It is known that the closure of an arbitrary $K_{\mathbf C}$-orbit on a flag manifold is expressed as a product of a closed $K_{\mathbf C}$-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 give its new applications to the study of domains arising from the duality.

#### Article information

Source
J. Math. Soc. Japan, Volume 57, Number 1 (2005), 157-165.

Dates
First available in Project Euclid: 13 October 2006

https://projecteuclid.org/euclid.jmsj/1160745819

Digital Object Identifier
doi:10.2969/jmsj/1160745819

Mathematical Reviews number (MathSciNet)
MR2114726

Zentralblatt MATH identifier
1076.14067

Keywords
Schubert cell flag manifold

#### Citation

GINDIKIN, Simon; MATSUKI, Toshihiko. A remark on Schubert cells and the duality of orbits on flag manifolds. J. Math. Soc. Japan 57 (2005), no. 1, 157--165. doi:10.2969/jmsj/1160745819. https://projecteuclid.org/euclid.jmsj/1160745819

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