  This paper describes the expected characteristic polynomial of the commutator
of randomly rotated matrices, in the context of the finite free probability
theory initiated by Marcus, Spielman, and Srivastava. The key technical
features are the use of Weingarten calculus to translate the random matrix
problem into one of combinatorial representation theory, followed by some
applications of the Goulden-Jackson immanant formula and the classical theory
of permutation modules.
