Timeline for Quadratic Casimir of fundamental irreps of simply-laced Lie algebras
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2016 at 14:36 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jun 9, 2016 at 14:35 | comment | added | Jim Humphreys | @brunch: Yes, I've edited accordingly in both places where I misquoted the definition. | |
| Jun 8, 2016 at 0:13 | comment | added | brunoh | A typo in your answer? the dual Coxeter number is defined using the highest short coroot right? | |
| Jul 7, 2014 at 20:33 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 4, 2014 at 9:49 | vote | accept | Peter Kravchuk | ||
| Apr 6, 2016 at 0:47 | |||||
| Jul 4, 2014 at 9:47 | comment | added | Peter Kravchuk | I tried using Freudenthal's formula, it indeed does simplify a lot for minuscule representations. It gives information about $(\varpi,\rho)$,however, I have not yet been able to relate it to squared norm of $\varpi$. Though I get some weird relations like $(\varpi,4\rho)=|\Delta|-|\Delta/\varpi|$, where $\Delta$ is the set of all roots, and $\Delta/\varpi$ is the set of roots obtained by deleting the node corresponding to $\varpi$ from Dynkin diagram, which is at least fun. | |
| Jul 3, 2014 at 19:57 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 3, 2014 at 6:04 | comment | added | Peter Kravchuk | Thanks! The minuscule property seems to be indeed very important here. I'll try finish your idea.. | |
| Jul 2, 2014 at 14:43 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Jul 2, 2014 at 13:55 | history | answered | Jim Humphreys | CC BY-SA 3.0 |