From: Michael Stone m-stone5 [snail] illinois.edu Mar 17 2012
Tableau symmetrizers are only "half orthogonal"
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In appendix B you claim to have proof that for standard-tableau
symmetrizers Y_a and Y_b, we have $Y_aY_b=Y_bYa= \delta_{ab} Y^2_a. What
is usually said to be true, however, is that they are only "half
orthogonal" In other words there is a total order on standard tableau of
a given shape such that Y_aY_b=0 if a