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Oct 15, 2018 at 8:26 history edited Uri Bader CC BY-SA 4.0
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Oct 15, 2018 at 4:20 vote accept Sean Eberhard
Oct 13, 2018 at 21:31 comment added YCor This is an answer for compact connected Lie groups. For arbitrary compact connected groups $G$, you need an additional argument using Peter-Weyl. Namely, if $w$ holds with positive measure, then it holds with positive measure in every quotient, and hence it holds identically in every Lie quotient, and by Peter-Weyl $G$ is projective limit of such Lie quotients, and hence $w$ holds in $G$. The argument also shows that $G$ is either abelian or contains a free subgroup, and if it's abelian and nontrivial, it satisfies $w$ iff $w$ belongs to $[F_k,F_k]$.
Oct 13, 2018 at 18:33 history edited Uri Bader CC BY-SA 4.0
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Oct 13, 2018 at 18:12 history edited Uri Bader CC BY-SA 4.0
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Oct 13, 2018 at 17:53 history answered Uri Bader CC BY-SA 4.0