Quotients of finite-dimensional operators by symmetry representations

A finite-dimensional operator which commutes with some symmetry group, admits quotient operators. Such a quotient operator is determined by the group action and by picking a certain representation of this group. We present a computationally simple construction to obtain quotients that reflect the structure of the original operators. These quotient operators allow us to generalize previous isospectral constructions of discrete graphs, as well as to provide tools for spectral analysis of finite-dimensional operators.

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This talk is based on a joint work with Gregory Berkolaiko, Christopher H. Joyner and Wen Liu.