Timeline for On the Weyl character formula
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 8, 2011 at 0:50 | vote | accept | Hugo Chapdelaine | ||
| Jan 7, 2011 at 23:20 | answer | added | user1504 | timeline score: 4 | |
| Jan 7, 2011 at 22:54 | answer | added | Hugo Chapdelaine | timeline score: 1 | |
| Jan 7, 2011 at 4:44 | comment | added | S. Carnahan♦ | You can find reasonably straightforward algebraic proofs (that apply in the more general Kac-Moody case) in Kac's Infinite dimensional Lie algebras or Kumar's book on Kac-Moody groups. | |
| Jan 7, 2011 at 1:25 | comment | added | Peter Woit | Oops, in the above comment, the second occurrence of "Weyl denominator formula" should be "Weyl integral formula". Also, I just remembered that there's a nice discussion of the Atiyah-Bott fixed point calculation I mentioned, see section 14.2 of Pressley and Segal's Loop Groups. | |
| Jan 7, 2011 at 1:09 | vote | accept | Hugo Chapdelaine | ||
| Jan 7, 2011 at 22:24 | |||||
| Jan 7, 2011 at 1:07 | comment | added | Hugo Chapdelaine | Thnaks a lot for your nice set of notes :) | |
| Jan 6, 2011 at 23:52 | answer | added | Jim Humphreys | timeline score: 16 | |
| Jan 6, 2011 at 23:50 | comment | added | Peter Woit | The first formula is the Weyl dimension formula, the second the Weyl denominator formula. They both follow easily from the Weyl character formula, and I wrote up some notes that give the standard somewhat geometric proof of this using the Weyl dimension formula here: math.columbia.edu/~woit/notes12.pdf A more sophisticated geometrical way to get the denominator formula would be to apply the Atiyah-Bott fixed point formula to the index-theory version of Borel-Weil-Bott for the trivial representation, as an index of an operator on the flag manifold. | |
| Jan 6, 2011 at 22:58 | history | asked | Hugo Chapdelaine | CC BY-SA 2.5 |