  We present a detailed analysis of the exact numerical spectrum of up to ten
interacting electrons in the first Landau level on the disk geometry. We study
the edge excitations of the hierarchical plateaus and check the predictions of
two relevant conformal field theories: the multi-component Abelian theory and
the W-infinity minimal theory of the incompressible fluids. We introduce two
new criteria for identifying the edge excitations within the low-lying states:
the plot of their density profiles and the study of their overlaps with the
Jain wave functions in a meaningful basis. We find that the exact bulk and edge
excitations are very well reproduced by the Jain states; these, in turn, can be
described by the multi-component Abelian conformal theory. Most notably, we
observe that the edge excitations form sub-families of the low-lying states
with a definite pattern, which is explained by the W-infinity minimal conformal
theory. Actually, the two conformal theories are related by a projection
mechanism whose effects are observed in the spectrum. Therefore, the edge
excitations of the hierarchical Hall states are consistently described by the
W-infinity minimal theory, within the finite-size limitations.
