Timeline for What is significant about the half-sum of positive roots?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 14, 2019 at 21:57 | comment | added | Francois Ziegler | This is the remark also made by Bott in (1988, eqs (17, 28, 30)), right? | |
| Nov 9, 2011 at 1:55 | history | edited | Allen Knutson | CC BY-SA 3.0 |
added 98 characters in body
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| Nov 8, 2011 at 4:12 | history | edited | Faisal | CC BY-SA 3.0 |
fixed typo in second formula
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| Nov 8, 2011 at 4:11 | comment | added | Faisal | A general remark: You get that formula if you apply A–B to the $\overline\partial$ operator acting on $\Omega^{(0,q)}(G/B,L_\lambda)$. In another paper Bott mentions that you can make the other formula for the Weyl denom (the one with $\rho$ in it!) show up if you approach things differently: $G/B$ is spin, so we can work with its (elliptic) Dirac operator $S^+ \to S^-$. Incidentally, the existence of a spin structure on $G/B$ is related to $\rho$: the canonical bundle of $G/B$ is $L_{-2\rho}$ so a holomorphic square root is given by $L_{-\rho}$, and this determines the spin structure. | |
| Nov 8, 2011 at 1:31 | history | answered | Allen Knutson | CC BY-SA 3.0 |