球面因子谱问题的群论观点
Group theory aspects of spectral problems on spherical factors
摘要：
Ray-Singer等谱定理（1971）被应用于三球面的齐次Clifford-Klein因子上的扭曲p-形式的拉普拉斯算子的一般谱函数。详细地给出了用四面体、八面体和二十面体甲板群的循环子群表示任意扭转的任意谱量所必需的诱导公式。此外，阿廷定理允许麦凯对应被获得。等谱定理示出产生的推导的Sunada建设是相当于后者的Pesce。
英文摘要：
The Ray-Singer isospectral theorem (1971) is applied to a general spectral function for Laplacians of twisted p-forms (say) on homogeneous Clifford-Klein factors of the three-sphere. The inducing formulae necessary to express any spectral quantity for any twisting in terms of those for cyclic subgroups of the tetrahedral, octahedral and icosahedral deck groups are detailed. Further, Artin's theorem allows the McKay correspondence to be obtained. The isospectral theorem is shown to yield a derivation of the Sunada construction which is equivalent to the later one by Pesce.
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