Timeline for Definition of $\textrm{GSpin}_{2n}$ and its root datum
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2019 at 3:24 | comment | added | LSpice | Your CSpin is the question’s GSpin, right? | |
| Nov 27, 2016 at 16:58 | comment | added | Marty | I've made edits based on the two comments above. | |
| Nov 27, 2016 at 16:57 | history | edited | Marty | CC BY-SA 3.0 |
Fix and edit based on comments
|
| Nov 27, 2016 at 15:05 | comment | added | nfdc23 | Marty, the construction and properties in your answer work over fields of all characteristics (even 2), and also work over any scheme with quadratic forms on vector bundles (where "non-degenerate" means that the quadratic form is fiberwise nonzero over the base and the associated projective quadric is smooth over the base). You might want to mention the link between the root system and the rank $d$ of $V$ (i.e., type B$_n$ if $d=2n+1 \ge 3$ and type D$_n$ if $d=2n \ge 4$). | |
| Nov 27, 2016 at 11:47 | comment | added | Mikhail Borovoi | You probably mean: "the only subtlety is in type $D_n$ with $n$ even". Indeed, when $n$ is odd the center of ${\rm Spin}_{2n}$ is isomorphic to $\mu_4$, so it has only one subgroup isomorphic to $\mu_2$. | |
| Nov 27, 2016 at 7:20 | history | answered | Marty | CC BY-SA 3.0 |