Between "very large" and "infinite" : The asymptotic representation theory
Between "very large" and "infinite" : The asymptotic representation theory
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在“非常大”和“无限”之间：渐近表示理论
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Vershik
中科院分区：
文献类型：
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作者：
A. Vershik
我说明了这个理论的历史根源，我后来把它称为“渐近表示理论”--这个理论可以看作是泛函分析、表示理论和更一般的概率论、渐近组合学、随机矩阵理论、动力学等的一部分。第一个也是非常具体的例子是J.von Neumann的一篇引人注目的(但被遗忘的)论文，我在这里试图将它与现代随机矩阵理论联系起来；第二个例子引用了H.Weyl关于对称群理论的一个重要思想。在最后一节中，我简要回顾了渐近表示理论的思想，它始于20世纪70年代，现在变得非常流行。我提到了几个重要的问题，并给出了一个参考文献列表(不完整)。但读者必须记住，这只是一个概要
I illustrate the historical roots of the theory which I called later “Asymptotic Representation Theory” – the theory which can be considered as a part functional analysis, representation theory, and more general – probability theory, asymptotic combinatorics, the theory of random matrices, dynamics, etc. The first and very concrete example is a remarkable (and forgotten) paper by J. von Neumann, which I try here to connect with the modern theory of random matrices; the second example is a quote of an important thought of H. Weyl about the theory of symmetric groups. In the last section I give a short review of the ideas of the asymptotic representation theory, which was developed starting from the 1970s, and now became very popular. I mention several important problems, and give a list (incomplete) of references. But the reader must remember that this is just a synopsis of