Timeline for Building a representation out of a generalized Verma module
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2013 at 13:34 | comment | added | S. Carnahan♦ | You may find some information in Kac-Raina's Bombay lectures. | |
| Feb 27, 2013 at 7:44 | comment | added | José Figueroa-O'Farrill | (cont'd) So what exactly do you need the explicit submodule for? If you want to gain intuition about this construction, perhaps you should look at how it works with a simple Lie algebra of small dimension, such as $\mathfrak{su}(2)$. | |
| Feb 27, 2013 at 7:43 | comment | added | José Figueroa-O'Farrill | The submodule in question might depend on the actual affine algebra that you are dealing with and in the actual highest weight. I am not sure that you can be very explicit in the general case. Already for finite simple Lie algebras, where the same construction applies, I am not aware of any explicit formula in general, but others will surely correct me if I'm wrong. Having said that, it is clear that the Verma module will have a maximal proper submodule and that the quotient, by definition, will be irreducible and of highest weight. | |
| Feb 27, 2013 at 5:44 | history | asked | Sven Cattell | CC BY-SA 3.0 |