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