Discretely Decomposable Restrictions of (,K)-Modules for Klein four symmetric pairs of Exceptional Lie Groups of Hermitian type
Discretely Decomposable Restrictions of (,K)-Modules for Klein four symmetric pairs of Exceptional Lie Groups of Hermitian type
复制标题
埃尔米特型异常李群克莱因四对称对的 (,K) 模的离散可分解限制
DOI：
10.1142/s0129167x20500019
复制
发表时间：
2020
影响因子：
0.6
通讯作者：
Haian He
中科院分区：
文献类型：
--
作者：
Haian He
Let (G, G(Gamma)) be a Klein four symmetric pair. The author wants to classify all the Klein four symmetric pairs (G, C-Gamma) such that there exists at least one nontrivial unitarizable simple (g, K)-module pi(K) that is discretely decomposable as a (g(Gamma), K-Gamma)-module. In this paper, three assumptions will be made. First, G is an exceptional Lie group of Hermitian type, i.e. C = E6(-14) or E7(-25). Second, G(Gamma) is noncompact. Third, there exists an element sigma is an element of Gamma corresponding to a symmetric pair of anti-holomorphic type such that pi(K) is discretely decomposable as a (g(sigma), K-sigma)-module.
