Lemma 7.4 is wrong as stated: the rank of D^T D can be smaller
than the rank of D. For example take the field C of complex
numbers and the matrix D^T = (1 i) of rank 1. We have D^T D = 0.
The result can be corrected by working with the real numbers, in
which case the restriction of the form to a complement of the
kernel of D is non-singular, since it is positive definite there.
This is sufficient for our purposes since the matrix D to which
this result is applied has integer entries.
There are some errors in the tables for A_5 on pages 91 and 92.
I am grateful to Serge Bouc for pointing this out.
He has a different approach
to computing the Cartan matrix described in his paper,
'Resolutions de foncteurs de Mackey'.
The errors originate with a mistake in the C_2,1 column of the matrix
\Psi for A_5 in characteristic 0 on page 91,
which should have the bottom two 0 entries both changed to 1.
On page 92 the C_2,1 row of the decomposition matrix should have the last two 0 entries changed to 1.
On page 92 the bottom right 4x4 square of the Cartan matrix should be
4222
2311
2132
2123