Matsuki correspondence for sheaves
Matsuki correspondence for sheaves
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松木滑轮对应
DOI：
10.1007/bf01232026
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发表时间：
1992
影响因子：
3.1
通讯作者：
K. Vilonen
中科院分区：
文献类型：
--
作者：
I. Mirkovic;Tohru Uzawa;Tohru Uzawa;K. Vilonen
本文将Matsuki对应[Mall]推广到层。这种对应关系的存在是由Kashiwara在[K]中证实的。设GR是一个约化李群，G是它的复化，KccG是极大紧子群KRcGR的复化，X是G的旗簇，同时给出了Matsuki [Ma 1，Ma 2，Ma 3]中某些结果的一个简单的几何证明. Matsuki在[Mall]中构造了X上Kc-轨道与GR-轨道之间的一个双射。本文证明了Kashiwara在[K]中所作结果的如下推广。
In this paper we extend the Matsuki correspondence [Mall to sheaves. The existence of this correspondence was conjectured by Kashiwara in [K]. At the same time we give a simple geometric proof of some of the results of Matsuki [Ma 1, Ma2, Ma3].Let GR be a reductive Lie group, G its complexification, Kc c G the complexification of a maximal compact subgroup KR c GR and X the flag variety of G. In [Mall Matsuki constructed a bijection between the Kc-orbits and GR-orbits on X. Here we prove the following extension of this result conjectured by Kashiwara in [K].