n 次中心对称量子图的可约性

Reducibility of n Subcentrally Symmetric Quantum Graphs

本文根据群的不可约表示给出了 n 次中心对称量子图上平方可积函数空间的分解及 n 次中心对称 量子图的商图,为量子图久期行列式的分解提供了新的思路,将原量子图的谱问题转化为商图的 谱问题,为等谱量子图的研究打下基础。

In this paper, according to the irreducible representation of the group, the decompo- sitions of the space of square integrable functions on n subcenter-symmetric quantum graphs and the quotient graph of n subcenter-symmetric quantum graphs are given. It provides a new idea for the decomposition of the long determinant of quantum graphs, and transforms the spectrum problem of the original quantum graph into the spectrum problem of the quotient graph, which lays a foundation for the research of isospectral quantum graphs.