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Finite dimensional representations of the Hanoi Towers group are used tocalculate the spectra of the finite graphs associated to the Hanoi Towers Gameon three pegs (the group serves as a renorm group for the game). These graphsare Schreier graphs of the action of the Hanoi Towers group on the levels ofthe rooted ternary tree. The spectrum of the limiting graph (Schreier graph ofthe action on the boundary of the tree) is also provided.

Schreier spectrum of the Hanoi Towers group on three pegs