Weyl tableau

This produces a non-standard Rumer function as shown by the representation on the right hand side. These non-standard functions, which correspond to a Rumer diagram in which the lines cross, are not used in calculations. A standard set of functions can be selected using the following procedure the open shell orbitals are represented by a 1 if their number occurs in the left hand column of the Weyl tableau or a 2 if it appears in the right hand column. Hence for the example above... 

Recall that for the U(n) electronic G-T bases, the G-T tableau, the Weyl tableau, the Paldus tableau or the 4-vector notation are all equivalent and there is a one-to-one correspondence between them. 

A less trivial example would be a 5-electron doublet function, constructed using 8 orbitals a particular Weyl tableau (one out of 1008) and its Gel fand equivalent might be... 

This problem is solved in terms of the Weyl tableaux (Fig. 7.1c) derived from the first Young tableau by inserting orbitals (or their indices) in the boxes in place of the electron indices thus, with 5 different orbitals, the products... 

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