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## Main Question or Discussion Point

Suppose I had some group G, and I could classify all of its irreducible K-representations for some K = R,C, or H. Given that information (how) can I classify its irreducible K-representations for all K.

i.e. suppose I knew all the irreducible real representations of G, (how) could I then get all the irreducible complex and quaternionic representations?

i.e. suppose I knew all the irreducible real representations of G, (how) could I then get all the irreducible complex and quaternionic representations?