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I have started an entry Majorana spinor with discussion of how the physicist’s concept going by that name is a real structure on a complex spin representation.
Initially I had wanted to just follow the note by Figueroa-O’Farrill, but either I am missing something or else there is a gap in the argument there.
So in particular at the moment I have just one direction “Majorana structure is real structure”, not the converse.
(And why is it that the proposition number cross referencing is again broken?)
I have expanded a good bit further at Majorana spinor.
Have added a section Examples – In dimensions 11, 10 and 9 with a bunch of relations between Majorana spinors in these dimensions that govern KK-compactification and T-duality between the corresponding supergravity theories.
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