Paul Schwahn on Nostr: They way I originally stated, before applying the triality automorphism, was this: ...

They way I originally stated, before applying the triality automorphism, was this:

The (-) half-spinor representation h₁₂ should preserve ℍ, and the vector representation h₂₃ should map it to its complement.

We have to be a bit careful when applying outer automorphisms, because they always also involve 𝐶 somewhere, and the explicit realization of each representation matters.