= Normalized highest-weight lowering formula
{title2=$|I,m\rangle=\sqrt{\frac{(I+m)!}{(2I)!(I-m)!}}J_-^{I-m}|I,I\rangle$}
In an <irreducible spin representation>, the <angular momentum lowering operator> has squared <norm> factor $(I+m)(I-m+1)$. Multiplying these factors from the <highest-weight vector> gives the factorial normalization displayed above. All factorial arguments are integers even when $I$ is half-integral. This produces a consistent positive-coefficient phase convention for all weight states and fixes signs in subsequent <isospin rotations>.
Back to article page
