ZhaoLiang on Nostr: Oh, John Carlos Baez has a nice paper explains this: This is basically linear ...

Oh, John Carlos Baez (npub1nf4…nqe4) has a nice paper explains this:
https://arxiv.org/abs/1101.5690

This is basically linear algebra: it's equivalent to say, a linear operator \(f\) on a complex vector space is the complexification of some real operator \(g\) of the underlying real vector space, if and only if \(f\) commutes with some 'conjugation' \(\tau\) of the complex space. In the quaternion case, you require \(\tau^2=-1\) instead of \(\tau^2=1\) in the real case.

(finally, replace the single \(f\) with the representation of a compact/finite group)