Detecting Representation Isomorphism Through Twisted Spectra

Abstract In this chapter, we give a spectral characterisation of isomorphism of induced representations. We also discuss strong isospectrality in the sense of Pesce (which, by a result of Sunada, is implied by weak conjugacy of subgroups), discuss an illustrative example of lens spaces due to Ikeda, and use the first result to give a spectral characterisation of weak conjugacy.