Timeline for Non-faithful irreducible representations of simple Lie groups
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2019 at 16:20 | vote | accept | Nadia SUSY | ||
| Apr 16, 2019 at 15:48 | answer | added | spin | timeline score: 11 | |
| Apr 16, 2019 at 15:17 | comment | added | Victor Protsak | In order to get a faithful representation of the spinor group, you must use a spinor representation somehow. So contrary to the impression you got from that comment, the standard representation is not atypical when viewed among all simple modules. What it is true that you can build all non-spinor fundamental weights by tensor products and decomposing. | |
| Apr 16, 2019 at 15:08 | answer | added | Victor Protsak | timeline score: 8 | |
| Apr 16, 2019 at 14:08 | history | edited | Victor Protsak | CC BY-SA 4.0 |
Corrected the title to match the question
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| Apr 16, 2019 at 13:19 | comment | added | Nadia SUSY | @Venkataramana: What does this look like dually on the Lie algebra side? | |
| Apr 16, 2019 at 13:17 | comment | added | Venkataramana | these are exactly the irreducible representations with highest weight (which is a character on a maximal torus $T$ of the simply connected compact group $G$), which is trivial restricted to the centre of G . | |
| Apr 16, 2019 at 12:47 | history | edited | Nadia SUSY | CC BY-SA 4.0 |
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| Apr 16, 2019 at 12:36 | history | edited | Nadia SUSY | CC BY-SA 4.0 |
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| Apr 16, 2019 at 12:19 | comment | added | Christoph Mark | AFAIK, all finite dimensional irreducible representations of $\mathfrak{g}$ are integrable. So, no need to worry about the difference between $\mathfrak{g}$ and $G$. AFAIK, for a integral positive weigth $\omega$, it will not give rise to a faithful representation if $(\omega,\beta^\vee)=0$ for a simple root $\beta$ (which seems equivalent to me). | |
| Apr 16, 2019 at 11:40 | review | Close votes | |||
| Apr 16, 2019 at 15:00 | |||||
| Apr 16, 2019 at 11:36 | history | edited | Nadia SUSY | CC BY-SA 4.0 |
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| Apr 16, 2019 at 11:36 | history | undeleted | Nadia SUSY | ||
| Apr 15, 2019 at 17:08 | history | deleted | Nadia SUSY | via Vote | |
| Apr 15, 2019 at 16:30 | history | asked | Nadia SUSY | CC BY-SA 4.0 |