Hyperspin and Hyperspace

A spinorial time-space ${\mathfrak{G}}_N$ that supports a Kaluza-Klein theory of gauge potentials can be made from $N$-component spinors of $\mathrm{SL}\mathrm{}(N,C)\mathrm{}$ in the way that the Minkowskian manifold (an ${\mathfrak{G}}_2$) is made from two-component spinors of $\mathrm{SL}\mathrm{}(2,C)\mathrm{}$. ${\mathfrak{G}}_N$ has dimension $n=N^2$ and fundamental form det $\left(k_{\Sigma \dot{\Sigma }}\right)=0\mathrm{}$ of degree $N$, not 2. ${\mathfrak{G}}_N$ unifies the photon and graviton with gauge quanta of all integer spins $s$ with $2<s<N$.