 Symmetric three-spin-one subspace

ID: symmetric-three-spin-one-subspace

The completely symmetric subspace of three spin-one systems has dimension

(3 3 + 3 - 1) = 10

and decomposes into one total-spin-

3

multiplet and one total-spin-

1

Sym^{3} (1) = 3 \oplus 1.

The highest-weight product state generates the seven-dimensional spin-

3

multiplet; its three-dimensional invariant complement is spin

1

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