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Jan 10, 2018 at 14:51 comment added Ben Green Paul, thanks for this. In fact, I think it's exactly the same proof, and in fact when I first came up with the proof I formulated it this way. Maybe it's more natural. Schur's lemma is hidden in the last step and I think < x, y > = (phi(x), y) with my notation. I don't know how you got to this argument, but for me it was via the fact that imprimitive => induced from G_1, and then look at how induced representations are given a unitary structure.
Jan 10, 2018 at 12:32 history answered Paul Broussous CC BY-SA 3.0