Representation theory of the group with 2 elements at workhttps://twitter.com/InertialObservr/status/1149413668905316352 …
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Yep, exactly! As do the symmetric/antisymmetric matrices or tensors, and so on. The formula f(x) = [f(x) + f(-x)]/2 + [f(x)-f(-x)]/2 is a a special case of decomposition into irreducible representations. The general case has an exact formula through character theory, too.
nice! I know that young tableux help for the decomposition of SU(N) groups, but are you saying that the characters can tell us the exact same thing for arbitrary groups?
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I can't find a source right now, but once you know a character χ of an irreducible representation, the operator of projection on this type of irrep is always given bypic.twitter.com/N6NbuhfEew
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oh wow that's super useful!
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