Timeline for A possible mistake in Kac's "Infinite Dimensional Lie Algebras"
Current License: CC BY-SA 3.0
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| Aug 14, 2012 at 18:08 | comment | added | Jim Humphreys | @Najdorf: Your question is a good one, which I can't answer. It's helpful to have a reference to Wan's book, which I hadn't thought of (though I think our library does own a copy). Please update your question if you get better insight than I got from reading Kac. | |
| Aug 14, 2012 at 7:54 | comment | added | Najdorf | Does Kac answer email? Actually I found what seems to be a full proof in "Introduction to Kac-Moody Algebra" by Zhexian Wan (Proposition 5.6, page 98). | |
| Aug 1, 2012 at 17:11 | comment | added | Jim Humphreys |
@Najdorf: See my added paragraph. I think I expanded correctly the steps sketched in the book, but then my attempt to invoke "density" was oversimplified. Since both $X$ and $X'$ are cones, maybe one can tweak my argument by adding that all positive real multiples of the chosen $h$ are also in $X$. Anyway, the argument given in the book is too sketchy even if it turns out to be basically correct (modulo a misprint). And there may not be any alternative sources to consult for c). Maybe it's time to consult Victor Kac directly?
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| Jul 31, 2012 at 18:11 | comment | added | Najdorf | Why are all integral points of X^{\prime} (defined as points where all simple roots give us integers) dense in the metric topology? I think it would be far from dense and actually discrete. | |
| Jul 29, 2012 at 21:55 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 29, 2012 at 21:25 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 29, 2012 at 20:39 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 29, 2012 at 15:25 | history | answered | Jim Humphreys | CC BY-SA 3.0 |