On certain domains in cycle spaces of flag manifolds
On certain domains in cycle spaces of flag manifolds
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关于标志流形循环空间中的某些域
DOI：
10.1007/s002080200326
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发表时间：
2002
影响因子：
1.4
通讯作者：
A. Huckleberry
中科院分区：
文献类型：
--
作者：
A. Huckleberry
抽象的。仿射齐性空间
与具有极大紧子群K的真实的半单李群G相关联的G^{\Bbb C}/K^{\Bbb C}$包含其真实的点的许多自然定义的{\it G}-不变邻域
$M_{\Bbb R} = G/K$，从不同的角度来看，这是令人感兴趣的。这里的通用岩泽域
$\Omega_I$是从入射几何的角度引入的，并导出了它的某些性质，例如，它是Stein，小林双曲型的，并且包含区域
由Akhiezer和Gindikin引入的$\Omega_{AG}$与定义的极大整环等价
切丛中与Killing度量相关的适应复结构的$\Omega_{adp}$
$TM_{\Bbb R}$。本文的主要目标之一是开发方法，从而更好地了解沃尔夫域
旗流形中开G-轨道D中的圈的$\Omega_W（D）$
$G^\Bbb C/P$。关键是舒伯特域
$\Omega_S（D）$是由Schubert循环定义的，它的维数与循环的维数是互补的。这些由包含岩泽因子AN的Borel子群定义，因此
$\Omega_S（D）$和
$\Omega_I$是密切相关的。
Abstract. The affine homogeneous space
$G^{\Bbb C}/K^{\Bbb C}$ associated to a real semi-simple Lie group G with maximal compact subgroup K contains a number of naturally defined{\it G}-invariant neighborhoods of its real points
$M_{\Bbb R} = G/K$ which are of interest from various points of view. Here the universal Iwasawa domain
$\Omega_I$ is introduced from the point of view of incidence geometry and certain of its properties are derived, e.g., it is Stein, Kobayashi hyperbolic and contains the domain
$\Omega_{AG}$ introduced by Akhiezer and Gindikin which is now known to be equivalent to the maximal domain of definition
$\Omega_{adp}$ of the adapted complex structure associated to the Killing metric in the tangent bundle
$TM_{\Bbb R}$. One of the main goals of the paper is to develop methods which lead to a better understanding of the Wolf domain
$\Omega_W(D)$ of cycles in an open G-orbit D in a flag manifold
$G^\Bbb C/P$. The key is the Schubert domain
$\Omega_S(D)$ which is defined by Schubert cycles of complementary dimension to the cycles. These are defined by a Borel subgroup containing an Iwasawa factor AN and consequently
$\Omega_S(D)$ and
$\Omega_I$ are closely related.