Coupling coefficients exchange symmetry

On the other hand, if the coupling coefficients are antisymmetric under exchange of the labels, the coupled state belongs to the antisymmetrized direct square, denoted as fa. This product space is restricted to combinations with ya yb, its dimension is equal to (n —1)/2. The characters for either part of the square can be determined separately. For the character of the [Pa part the derivation runs as follows one first applies a symmetry operator to an arbitrary antisymmetric function. The ket product Paya l)) Payb(2)) will be abbreviated here as ya(l)yh(2). 

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