A necessary condition for discrete branching laws for Klein four symmetric pairs
A necessary condition for discrete branching laws for Klein four symmetric pairs
复制标题
克莱因四对称对离散分支律的必要条件
DOI：
10.1142/s0219498823500391
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发表时间：
2021-10
影响因子：
0.8
通讯作者：
Haian He
中科院分区：
文献类型：
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作者：
Haian He
给出了Klein四对称对[公式：见正文]满足条件（D.D.）的一个必要条件;也就是说，至少存在一个无限维的简单[Formula：see text]-模，它可以离散地分解为[Formula：see text]-模。这项工作是[克莱因四对称对离散分支定律的准则及其对[公式：见文本]的应用，Int. J. Math. 31（6）（2020）2050049]的延续。此外，我们还定义了相应的Klein四对称对，并利用这些工具计算出一类Klein四对称对不满足条件（D.D.）;例如，[公式：见正文]。
We show a necessary condition for Klein four symmetric pairs [Formula: see text] satisfying the condition (D.D.); that is, there exists at least one infinite-dimensional simple [Formula: see text]-module that is discretely decomposable as a [Formula: see text]-module. This work is a continuation of [A criterion for discrete branching laws for Klein four symmetric pairs and its application to [Formula: see text], Int. J. Math. 31(6) (2020) 2050049]. Moreover, we define associated Klein four symmetric pairs, and we may use these tools to compute that a class of Klein four symmetric pairs do not satisfy the condition (D.D.); for example, [Formula: see text].