9 Apr 2003
Dear Prof. Cvitanovic,

I have a short group theory
related question that has been bothering me for some time.

The question concerns non-standard fillings of tableaux, that is,
tableaux in which the numbers do not increase along rows and columns. 
When interpreting the tableaux as projection operators, such fillings
still make sense. However, a projector associated with a non-standard
filling now has to be expressible as a sum of projectors associated to
standard fillings. As an example, for a 

    XX
    X
    X

tableau, we have 

    21 =  +   12    -   13    +   14
    3         3         2         3
    4         4         4         2

These coefficients can of course be obtained by brute force, by
writing out the projectors on the lhs and rhs, and solving the
resulting system of linear equations. However, I'd expect that someone
probably has figured out a more clever way to do it.

Are you aware of a clever reduction algorithm that achieves such
decomposition of non-standard tableaux in terms of standard ones?

Kasper Peeters

MPI/AEI fuer Gravitationsphysik
Am Muehlenberg 1
14476 Golm
Germany
				kasper.peeters@aei.mpg.de