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Oct 13, 2018 at 0:50 history edited Sean Eberhard CC BY-SA 4.0
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Oct 12, 2018 at 19:20 comment added YCor I didn't use Lie theory, but indeed used both Peter-Weyl, and facts of real algebraic geometry, so this is indeed more elementary.
Oct 12, 2018 at 18:06 history answered Sean Eberhard CC BY-SA 4.0