Semi-invariant Vectors Associated with Holomorphically Induced Representations of Exponential Lie Groups
Semi-invariant Vectors Associated with Holomorphically Induced Representations of Exponential Lie Groups
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与指数李群的全纯诱导表示相关的半不变向量
DOI：
10.1007/978-3-030-78346-4_6
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Junko Inoue
中科院分区：
文献类型：
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作者：
Junko Inoue
从复子代数和实线性形式出发，研究了指数群G与李代数的全纯诱导表示在分布意义下的Frobenius互易性。我们处理了一些群的例子，并给出了一个新的例子，使得空间非零，互易性在下面的意义下不成立。在我们的例子中，G的不可约表示集，使得半不变的广义向量空间是非零的，并不符合与分解有关的Plcherel测度的支持。
We study Frobenius reciprocity in distribution sense for holomorphically induced representationsof exponential groupsGwith Lie algebras, from complex subalgebrasofand real linear formsf. We treat some examples of groups, and give a new examplesuch that the spaceofis non-zero, and the reciprocity does not hold in the following sense. In our example, the setof irreducible representations ofG, such that the spaces of semi-invariant generalized vectors are non-zero does not coincide with the support of the Plancherel measure associated with the decomposition of.