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A criterion for discrete branching laws for Klein four symmetric pairs and its application to E6(−14)
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2020-03-16 , DOI: 10.1142/s0129167x20500494
Haian He 1
Affiliation  

Let [Formula: see text] be a noncompact connected simple Lie group, and [Formula: see text] a Klein four-symmetric pair. In this paper, we show a necessary condition for the discrete decomposability of unitarizable simple [Formula: see text]-modules for Klein for symmetric pairs. Precisely, if certain conditions hold for [Formula: see text], there does not exist a unitarizable simple [Formula: see text]-module that is discretely decomposable as a [Formula: see text]-module. As an application, for [Formula: see text], we obtain a complete classification of Klein four symmetric pairs [Formula: see text], with [Formula: see text] noncompact, such that there exists at least one nontrivial unitarizable simple [Formula: see text]-module that is discretely decomposable as a [Formula: see text]-module and is also discretely decomposable as a [Formula: see text]-module for some nonidentity element [Formula: see text].

中文翻译:

克莱因四对称对离散分支律的判据及其在 E6(-14) 中的应用

令[公式:见正文]为非紧连通单李群,[公式:见正文]为克莱因四对称对。在本文中,我们为 Klein 的对称对的可统一简单 [公式:见文本]-模块的离散可分解性展示了一个必要条件。准确地说,如果对[公式:见文本]成立某些条件,则不存在可离散地分解为[公式:见文本]-模块的可统一的简单[公式:见文本]-模块。作为应用,对于[公式:见文],我们得到克莱因四对称对[公式:见文]的完整分类,其中[公式:见文]是非紧的,使得至少存在一个非平凡可统一的简单[公式:见文本]-模块,可离散分解为 [公式:见文本]-模块,也可离散分解为 [公式:
更新日期:2020-03-16
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