Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs
Multiplicity-free Theorems of the Restrictions of Unitary Highest Weight Modules with respect to Reductive Symmetric Pairs
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DOI：
10.1007/978-0-8176-4646-2_3
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发表时间：
2006-06
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影响因子：
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通讯作者：
Toshiyuki Kobayashi
中科院分区：
文献类型：
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作者：
Toshiyuki Kobayashi
复分析方法在无重数表示的研究中有着广泛的应用。本文特别讨论了它在关于约化对称对限制最高权模问题中的应用。我们提出了一些无重性分支定理，包括一些已知结果的无重性，如张量积的Clebsh-Gordan-Pieri公式，Hermitian对称空间的Plancherel定理（也适用于线丛情况），Hua-Kostant-SchmidK型公式，以及Vershik-Gelfand-Graev意义下的正则表示。我们的方法工程在一个统一的方式为有限和无限维的情况下，为离散和连续的频谱，并为经典和例外的情况下。
The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known results such as the Clebsh–Gordan–Pieri formula for tensor products, the Plancherel theorem for Hermitian symmetric spaces (also for line bundle cases), the Hua–Kostant–SchmidK-type formula, and the canonical representations in the sense of Vershik–Gelfand–Graev. Our method works in a uniform manner for both finite and infinite dimensional cases, for both discrete and continuous spectra, and for both classical and exceptional cases.