Timeline for Why do the adjoint representations of three exceptional groups have the same first eight moments?
Current License: CC BY-SA 3.0
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| Feb 24, 2016 at 16:55 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Feb 24, 2016 at 16:53 | vote | accept | Will Sawin | ||
| Feb 24, 2016 at 16:48 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Feb 23, 2016 at 22:34 | answer | added | Kim Morrison | timeline score: 14 | |
| Feb 20, 2016 at 17:27 | comment | added | Will Sawin | @QiaochuYuan Sure. One could write a category in terms of generators and relations, remove some of the relations and note that the moment sequence simplifies, and then argue that the relations only affect moments starting at the $N$th one. This is precisely how I calculated the stable moments of $A_n$ - take the free symmetric monoidal linear category with duals on an object of dimension $n+1$, then remove the dimension $n+1$ condition and calculate the right $\operatorname{Hom}$. But the details in this case are beyond me. | |
| Feb 20, 2016 at 16:28 | comment | added | Qiaochu Yuan | These numbers are dimensions of spaces of morphisms between tensor powers of representations, so you could try to give direct descriptions of the categories of representations - I believe they have universal descriptions along the lines of "the free symmetric monoidal linear category with duals on an object of some dimension + a non-degenerate 3-form" but I'm not sure of the exact details. (So a reason for the 9th moments to differ is different behavior of 3 copies of the 3-form.) | |
| Feb 20, 2016 at 15:31 | history | edited | Will Sawin |
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| Feb 20, 2016 at 15:10 | history | asked | Will Sawin | CC BY-SA 3.0 |