Timeline for Update on list of open problems for Cherednik/Symplectic Reflection Algebras
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16, 2014 at 15:10 | comment | added | Stephen | OK, thanks! I should edit the answer a bit when I have some time, and among other thigns I'll fix that. | |
| Aug 16, 2014 at 13:19 | comment | added | Ben Webster♦ | I'd certainly accept "crystal combinatorics." I'll think about your question about $L_c(\mathrm{triv})$; I'll admit that working through the combinatorics is some work, but I would say it's an order of magnitude less than affine KL polynomials. | |
| Aug 15, 2014 at 22:16 | vote | accept | Zahlendreher | ||
| Aug 15, 2014 at 22:16 | vote | accept | Zahlendreher | ||
| Aug 15, 2014 at 22:16 | |||||
| Aug 15, 2014 at 16:17 | comment | added | Stephen | @BenWebster Perhaps I should have written "crystal combinatorics" instead of "KL combinatorics"? I would be interested to know if it's possible to recover Pavel Etingof's classification of when $L_c(\mathrm{triv})$ is finite dimensional for $G(2,1,n)$ from what Roman and Ivan did (or from what Ivan has done since). | |
| Aug 14, 2014 at 17:19 | comment | added | Stephen | Well, ok, when is the trivial lowest weight irreducible finite dimensional? It's my impression from talking to Ivan that even this question is not so easy to answer. It would be interesting for me, at least, to know if the set of parameters for which it is can have components of codimension more than two in the parameter space! | |
| Aug 14, 2014 at 16:02 | comment | added | Ben Webster♦ | At least for G(r,1,n), one doesn't need Kazhdan-Lusztig combinatorics to see which simples are finite dimensional, though one does need them to calculate the dimension. The description of finite dimensional should follow from Bezrukavnikov-Losev. | |
| Aug 14, 2014 at 15:38 | history | answered | Stephen | CC BY-SA 3.0 |