  We determine spectral measures for some nimrep graphs arising in subfactor
theory, particularly those associated with SU(3) modular invariants and
subgroups of SU(3). Our methods also give an alternative approach to deriving
the results of Banica and Bisch for ADE graphs and subgroups of SU(2) and
explain the connection between their results for affine ADE graphs and the
Kostant polynomials. We also look at the Hilbert generating series of
associated pre-projective algebras.
