Timeline for Representation R where the center of Spin group acts trivially on R
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 19, 2019 at 4:58 | comment | added | Michael Murray | Presumably in the odd case the centre is the kernel of the projection to SO(n) ? Then the representations trivial on the centre are the representations of SO(n). Maybe for the others you can see this from the representation ring of Spin(n) by direct calculation of the action of the centre ? You should be able to find the representation ring of Spin(n) in lots of places. For example Husemoller's Fibre Bundles I know describes it but otherwise a book on representations of compact Lie groups. | |
| Dec 19, 2019 at 2:54 | comment | added | annie marie cœur | en.wikipedia.org/wiki/Spin_group#Center | |
| Dec 19, 2019 at 2:53 | comment | added | annie marie cœur | Should be $\operatorname{Spin}(n,\mathbf{R})$. But I follow the Wikipedia for the center group | |
| Dec 19, 2019 at 2:52 | history | edited | annie marie cœur | CC BY-SA 4.0 |
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| Dec 18, 2019 at 23:38 | comment | added | Michael Albanese | I am confused by your second sentence. By $\operatorname{Spin}(n, \mathbb{C})$, do you mean a double cover of $SO(n, \mathbb{C})$? This is not the same as $\operatorname{Spin}(n)$. | |
| Dec 18, 2019 at 23:28 | history | asked | annie marie cœur | CC BY-SA 4.0 |