Timeline for Some confusion about weights and roots in parabolic root systems
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 25, 2019 at 4:51 | comment | added | D_S | Thank you. I don't know why this part of Arthur's notes is so hard for me! | |
| Jan 25, 2019 at 2:46 | comment | added | LSpice | @D_S, my explanation on dual bases was confusing, if not downright wrong, so I deleted it. I will try to post a better one tomorrow. | |
| Jan 24, 2019 at 20:56 | history | edited | LSpice | CC BY-SA 4.0 |
Corrected the order-reversing bijection
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| Jan 20, 2019 at 0:23 | comment | added | D_S | Granting that the "coroots" $\Delta_P^{\vee}$ are defined to be the basis of $\mathfrak a_P^G$ which is dual to the basis of $\mathfrak a_P^{G \ast}$ obtained by taking the image of the weights $\varpi_{\alpha} : \alpha \in \Delta_0 - \Delta_0^P$ into $\mathfrak a_P^{G \ast}$, it isn't clear to me why $\Delta_P^{\vee}$ is the same as the restrictions to $\mathfrak a_P^G$ of the ordinary coroots $\beta^{\vee} : \beta \in \Delta_0 - \Delta_0^P$ as Arthur says. In general, taking dual bases and projecting to subspaces does not result in dual bases. | |
| Jan 17, 2019 at 20:56 | comment | added | D_S | The part I cited is on page 26 of the paper you linked. | |
| Jan 17, 2019 at 18:55 | history | answered | LSpice | CC BY-SA 4.0 |