Some Considerations on Global Symmetry

If the recently discovered $Y^{*}$ state is related to the $T=\frac{3}{2}$, $J=\frac{3}{2}$ resonance in $\pi p$ scattering, global symmetry considerations should become relevant. In this paper, global symmetry is discussed with a view to understanding its group structure. Also discussed is a possibility of reconciling the conflict, pointed out by Pais, between certain experimental results and global symmetry. The partial widths of the $Y^{*}$ state are calculated and also those of the companion excited states $Z^{*}$ and ${\Xi }^{*}$. A generalization of the quantum number $G$ is discussed.