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MacKey constructed a set of induced representation character formulas tocalculate the sum of different powers of the eigenvalues of a matrix withfinite group symmetry. We show that these results of MacKey can be used toderive the stability condition, m > Cn3, of Maxwell using his symmetric modelfor a ring of Saturn, as a collection of n identical unit mass particlesrevolving round Saturn, which has mass m, in a circular orbit.

An Induced Representation Method for Studying the Stability of Saturn's Ring