Timeline for Realizing higher level Fock spaces
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 4, 2010 at 21:14 | comment | added | David Hill | I'll have to think about it more, but my first instinct is that the answer is no. The $k$-multipartition description comes from tensoring together $k$ level 1 representations, each parametarized by partitions. In my paper, I skipped the big space and defined the action in one shot. Then again, maybe the translation is not too bad? I'll think some more. | |
| Oct 4, 2010 at 20:40 | vote | accept | Oded Yacobi | ||
| Oct 4, 2010 at 20:37 | comment | added | Oded Yacobi | Thank you very much for this link. I think this is very close to what I was looking for, although I haven't had a chance to look at it closely yet. A question: from what I understand the level k Fock space has a basis indexed by k multi-partitions. Is this "visible" in your construction? | |
| Oct 4, 2010 at 19:38 | comment | added | David Hill | I guess I should say that it is straighforward to extend the $\mathfrak{gl}_\infty$-module I mentioned above to $a_\infty$ in a way analogous to the Kac-Raina level 1 extension. So, you get an action of $\hat{\mathfrak{sl}}_p$ on the Fock space. The problem is that it is not generally irreducible as a $\hat{\mathfrak{sl}}_p$-module. | |
| Oct 4, 2010 at 19:22 | history | answered | David Hill | CC BY-SA 2.5 |