On Rationality Properties of Involutions of Reductive Groups
On Rationality Properties of Involutions of Reductive Groups
复制标题
论约简群的合合有理数性质
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
S. Wang
中科院分区：
文献类型：
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作者：
A. Helminck;S. Wang
介绍。设k为特征非二的域，G为连通的线性约化k群。G的k对合θ是指G的二阶k自同构θ。对于k = R， C或代数闭场，这种对合已经从不同的兴趣中得到了广泛的研究。如[8,18,28]所示，与还原性群体表征理论的互动是最有益的。仿射对称空间的离散级数在算术子群[27]上同调中的应用引起了q -对合的研究。本文讨论了一般k-对合的合理性问题。在这里，我们概括了大多数早期的结果[15,16,23,29]，锐化了一些并添加了新的结果。设H是G的对合θ的不动点群G θ的开子群
Introduction. Let k be a field of characteristic not two and G a connected linear reductive k-group. By a k-involution θ of G, we mean a k-automorphism θ of G of order two. For k = R, C or an algebraically closed field, such involutions have been extensively studied emerging from different interests. As manifested in [8, 18, 28], the interactions with the representation theory of reductive groups are most rewarding. The application of discrete series of affine symmetric spaces to the cohomology of arithmetic subgroups [27] invites the study of Q-involutions. In the present paper, we give a treatment on rationality problems of general k-involutions. Here we generalize most of the earlier results [15, 16, 23, 29], sharpen some and add new ones. Let H be an open subgroup of the fixed point group G θ of an involution θ of G. In