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May 20, 2011 at 19:22 comment added David E Speyer Yes, I think there is no way of avoiding some difficult analysis there. That's the main reason I said I wasn't sure this was what you wanted.
May 20, 2011 at 18:39 comment added Fedor Petrov Thanks, this is nice argument, the onliest problem why it is not appropriate for my students is that they do not know the proof of Peter-Weyl theorem, which requires some functional analysis (or it actually does not? the proof which I know requires some properties of compact operators.)
May 19, 2011 at 23:02 history edited David E Speyer CC BY-SA 3.0
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May 19, 2011 at 23:02 comment added David E Speyer No, but I used W for two things: the Weyl group and the hypothetical representation in the second paragraph. I'll change the later use to $U$.
May 19, 2011 at 22:58 comment added Keerthi Madapusi Did you switch from $V$ to $W$ at some point?
May 19, 2011 at 22:56 history edited David E Speyer CC BY-SA 3.0
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May 19, 2011 at 22:48 history answered David E Speyer CC BY-SA 3.0