Non-Abelian Harmonic Analysis
Non-Abelian Harmonic Analysis
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DOI：
10.1007/978-1-4613-9200-2
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
R. Howe;Eng-Chye Tan
中科院分区：
文献类型：
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作者：
R. Howe;Eng-Chye Tan
这本书主要讨论特殊线性群8L(2，1R)的表示理论，以及该理论的一些应用。事实上，重点放在应用程序上；这本书在编写十年时的临时标题是“一些你可以用8L(2)做的事情”。这些应用有的是表象理论之外的，有的是表象理论本身。表象理论之外的主题大多具有重要的经典意义(傅立叶分析、拉普拉斯方程、惠更斯的打印原理、遍历理论)，而表象理论内部的主题主要涉及Harish-Chandra发展半单群上的调和分析的核心主题(他的限制定理、正则性定理、特征标公式、矩阵系数的渐近衰减和调和)。我们希望通过说明(没有冗长的问题)表征理论如何为熟悉的话题提供新的视角，并通过对表征理论本身的一些重要主题的一些洞察，来吸引表征理论中的非专业人士。特别是，我们希望这本书推广哈里什-钱德拉的限制公式，该公式除了是他工作的基础外，也是欧几里德空间上傅里叶分析的一个美丽的例子。我们也希望表征理论家喜欢看到他们的主题如何被使用的例子，并将被关于表征理论问题的一些观点所启发。
This book mainly discusses the representation theory of the special linear group 8L (2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was" Some Things You Can Do with 8L (2)." Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.