G-parity of an isospin multiplet
= G-parity of an isospin multiplet
{c}
{title2=$G=\eta(-1)^I$}
For integer <isospin> $I$ and neutral-state <charge conjugation> value $\eta$, the entire <isospin multiplet> has $G=\eta(-1)^I$. Both charge conjugation and the second-axis half-turn reverse the first and third generators, so their product commutes with the full isospin algebra. Evaluate it on the $M=0$ state and use ladder connectivity to obtain the value for every $M$.