Irreducibility of (anti)self-dual reps

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  • Thread starter gentsagree
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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!
 

Answers and Replies

  • #2
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It would be easier to argue if you supply a more detailed framework. In general a representation is irreducible if there are no proper submodules. So you could take a basis vector and show that its orbit is the whole module.
 

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