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## Main Question or Discussion Point

Imagine we are talking about the group SO(4). The second rank antisymmetric representation is reducible into self-dual and antiself-dual representations. I think a good way to visualise this is by noticing that the projection of [itex] \Lambda^{2}V [/itex] into self and antiself dual subspaces commutes with the action of SO(4).

However, how can I show that those subspaces are themselves irreducible?

Thanks!

However, how can I show that those subspaces are themselves irreducible?

Thanks!