Timeline for What role does the "dual Coxeter number" play in Lie theory (and should it be called the "Kac number")?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2019 at 17:59 | answer | added | Theo Johnson-Freyd | timeline score: 9 | |
| Jun 9, 2016 at 14:34 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jun 9, 2016 at 14:32 | comment | added | Jim Humphreys | @brunch: Yes, I tend to forget this essential dualization, so I've edited my question. (Note that you need to add 1 to the sum of coefficients, which in the Kac definition comes from the "extra" node in the affine setting.) | |
| Jun 8, 2016 at 0:05 | comment | added | brunoh | I suspect there is a typo in your question : the dual Coxeter number is the sum of coefficients of the highest short coroot not of the highest short root. | |
| Dec 18, 2011 at 4:27 | answer | added | brandyn | timeline score: 3 | |
| Feb 28, 2011 at 16:19 | comment | added | Jim Humphreys |
@Skip: Belated thanks for your comment. I had forgotten about that discussion in S-S, which was aimed at computing the discriminant of the Killing form relative to a Chevalley basis. Leaving aside their notational choices, this adds weight to the argument that the "dual Coxeter number" doesn't really need a name but only a symbol such as the currently common $h^\vee$ together with a brief reminder of what the symbol means.
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| Jun 4, 2010 at 16:05 | comment | added | Skip | Just a historical note to add to the dates mentioned above: The dual Coxeter number makes an appearance in Springer-Steinberg's 1970 paper "Conjugacy classes" on pages E-12 through E-15, where it is defined and used to calculate the Killing form on the Cartan subalgebra. | |
| May 24, 2010 at 15:01 | vote | accept | Jim Humphreys | ||
| May 23, 2010 at 22:33 | answer | added | Peter Tingley | timeline score: 9 | |
| May 23, 2010 at 16:06 | answer | added | David Ben-Zvi | timeline score: 28 | |
| May 22, 2010 at 18:59 | answer | added | Bruce Westbury | timeline score: 1 | |
| May 22, 2010 at 17:52 | history | asked | Jim Humphreys | CC BY-SA 2.5 |