表示论的等谱成果：量子图与鼓
The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
摘要：
我们提出了一种方法，使一个构造等谱对象，如量子图和鼓。该方法的一个方面是基于表示理论的论点，显示和证明。补充部分涉及组装技术，既有一般陈述，又有示范。为此，量子图是最有用的。我们开发的直觉，站在背后的建设，以及生产等光谱对象的实际技能。我们讨论的理论影响，其中包括作为一个特殊的情况下，这种方法所产生的Sunada的定理的isospectrality。一个画廊的新的等谱的例子和一些已知的例子表明，从我们的理论。
英文摘要：
We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For that purpose, quantum graphs are grist to the mill. We develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects. We discuss the theoretical implications which include Sunada's theorem of isospectrality arising as a particular case of this method. A gallery of new isospectral examples is presented and some known examples are shown to result from our theory.
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