From: Henriette Elvang elvang [snail] umich.edu Aug 31 2012
To: Michael Stone
Error in Appendix B
===================
You are correct that our Young-projectors are not in general orthogonal,
but only half-orthogonal. Stembridge refers back to Young for the
statement that the tableaux
A= 123 B= 135
45 24
are only half-orthogonal. It is indeed not hard to demonstrate that
with our construction $P_B P_A = 0$ while $P_A P_B \ne 0$. So our
construction yields projectors that are half-orthogonal and not fully
orthogonal.
The short argument given in appendix B is therefore too good to be true;
we will revise it and correct the statement about orthogonality. The
property we actually use is the orthogonality between projectors arising
from distinct Young diagrams; we will clarify this when revising the
text.
Thank you for pointing this error out to us.