Timeline for Irreps which aren't highest-weight modules.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 23, 2012 at 15:38 | comment | added | Alain Valette | Bienvenue Monsieur Swiat! | |
| Apr 23, 2012 at 15:07 | comment | added | B R | Igor, that's good to know. By the way, you are correct that the answer is "of course not" for f.d. reps. | |
| Apr 23, 2012 at 14:58 | comment | added | Igor Makhlin | 2BR. Oh, yes, that would explain the misunderstanding. Just in case: in my question I'm not assuming the irreps to be finite dimensional. Otherwise the answer is "of course not", AFAIU. | |
| Apr 23, 2012 at 14:54 | comment | added | Igor Makhlin | a) Well, yeah. And why exactly? =) b) Since I'm considering Lie algebras, I assume you're talking about the trace representation: $$g(v)=k\mathrm{Tr}(g)v, k\in\mathbb C.$$ Then your statement (without the part about $k$ being an integer) is obviously true for the irreps which are highest-weight modules. Can't say why it holds for any other irrep though. | |
| Apr 23, 2012 at 14:51 | comment | added | B R | Are you assuming the representations are finite dimensional? | |
| Apr 23, 2012 at 14:37 | history | answered | Swiat Gal | CC BY-SA 3.0 |