Representations of the Affine Transformation Groups Acting Simply Transitively on Siegel Domains
Representations of the Affine Transformation Groups Acting Simply Transitively on Siegel Domains
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西格尔域上简单传递的仿射变换群的表示
DOI：
10.1006/jfan.1999.3463
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发表时间：
1999
影响因子：
1.7
通讯作者：
H. Ishi
中科院分区：
文献类型：
--
作者：
H. Ishi
设G是作用在Siegel整环D上的可裂可解李群。本文考虑G在D上全纯函数的Hilbert空间上实现的不可约酉表示。我们确定所有这样的希尔伯特空间，通过连接它们与正Riesz分布的对偶锥，并通过傅立叶-拉普拉斯变换来描述它们。利用轨道方法对G的表示进行了分类。
Let G be the split solvable Lie group acting simply transitively on a Siegel domain D. We consider irreducible unitary representations of G realized on Hilbert spaces of holomorphic functions on D. We determine all such Hilbert spaces by connecting them with positive Riesz distributions on the dual cone and describe them through the Fourier–Laplace transform. Moreover we classify the representations of G by making use of the orbit method.