This is an exercise that I am stuck on and any advice on this proof would thus be greatly appreciated.
2026-04-03 14:31:00.1775226660
Prove that if V is an irreducible representation of a lie algebra, then the dual representation V' must be irreducible.
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Hint: Suppose that $U$ is an invariant subset of the dual, show that $\{x\in V:u(x)=0,u\in U\}$ is invariant.