Permutation Symmetries of Generalized Beta Interactions

The permutation symmetries of the even and the odd beta couplings are investigated for $2^n$-rowed spinors. In the usual four-rowed case there are two quadratic forms which are independent of the order of writing the spinors. In the usual even case these are $\Sigma {C_{\sigma }}^4{\left|g_{\sigma }\right|}^2$ and ${|g_S+4\mathrm{}{g}_A-g_P|}^2$; in the odd case, $\Sigma {C_{\sigma }}^4{\left|u_{\sigma }\right|}^2$ and $\frac{1}{2}{|u_S+u_P|}^2+6\mathrm{}{\left|u_T\right|}^2$. For eight-rowed spinors with even couplings there are two completely antisymmetric forms; with odd couplings there is again only one.