Vanishing theorems for lie algebra cohomology and the cohomology of discrete subgroups of semisimple lie groups
Vanishing theorems for lie algebra cohomology and the cohomology of discrete subgroups of semisimple lie groups
复制标题
李代数上同调和半单李群离散子群上同调的消失定理
DOI：
10.1016/s0001-8708(81)80005-9
复制
发表时间：
1981
影响因子：
1.7
通讯作者：
W. Schmid
中科院分区：
文献类型：
--
作者：
W. Schmid
设G是具有有限中心的连通半单李群，FcG是离散子群使得F\G是紧的，F是有限维G-模.本文给出了Borel和Wallach [6]及Zuckerman [34]关于系数在F中的F的上同调群的一个最近消失定理的新证明。证明基于Harish-Chandra模和伯恩斯坦等人~范畴中模的rt-上同调群的消失定理。[3]的文件。这些结果还有其他应用，将在其他地方讨论。我将开始陈述主要定理。一劳永逸地，我固定了一个极大紧子群KcG。则F在对称空间G/K上适当地间断作用。G-模F产生丛
Let G be a connected semisimple Lie group with finite center, Fc G a discrete subgroup such that F\G is compact, and F a finite dimensional G-module. In this paper, I shall present a new proof of a recent vanishing theorem of Borel and Wallach [6] and Zuckerman [34], about the cohomology groups of F with coefficients in F. The proof is based on vanishing theorems for the rt-cohomology groups of Harish-Chandra modules and of modules in the category~ of Bernstein et al.[3]. These results have other applications, which will be taken up elsewhere. I shall begin with a statement of the main theorem. Once and for all, I fix a maximal compact subgroup K c G. Then F acts properly discontinuously on the symmetric space G/K. The G-module F gives rise to a bundle