Timeline for Miura transform for W-algebras of exceptional type
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 28, 2011 at 17:33 | comment | added | Yuji | By improving the program now the expression is about ~0.9MB :) | |
| Oct 27, 2011 at 14:41 | comment | added | Yuji | Thanks, I managed to get the generators. The degree-9 one was not so bad; but the degree-12 one, when dumped to a file, has ~ 100MB as an expression. Oh Buddha. | |
| Oct 26, 2011 at 16:19 | comment | added | Alexander Braverman | Good luck, Yuji! | |
| Oct 26, 2011 at 13:28 | comment | added | Yuji | Thanks everyone; I know got the generators at degree 2 and 5. Now I need those at degree 6, 8, 9 and 12 :p | |
| Oct 26, 2011 at 9:43 | comment | added | Reimundo Heluani | I think he wants the fields for each exponent of $E6$ together with their OPE. I don't think you'll find those Yuji, at least at the principal nilpotent. In the case of the minimal nilpotent, Kac and Wakimoto have explicit formulas in this paper | |
| Oct 26, 2011 at 6:07 | comment | added | Alexander Braverman | Do you want just generators, or generators and relations? | |
| Oct 26, 2011 at 6:01 | comment | added | Yuji | Yes you're right. Physicists cover their lack of deep thinking by lots of explicit calculation:p I've been using that approach to find generators of W(E6), but that's still quite messy. That's why I asked the question here. | |
| Oct 26, 2011 at 5:48 | comment | added | Alexander Braverman | Since I don't believe in explicit formulas, I won't be able to say anything intelligent here:) One remark, though: you can describe the image of the W-algebra without the screening operators. It is just equal to the intersection over all simple roots of things like Virasoro$\otimes$Heisenberg of smaller rank (I hope it is clear what I mean) | |
| Oct 26, 2011 at 4:26 | comment | added | Yuji | Thank you, but my main problem is to explicitly write down the subalgebra commuting with the screening operators. For A and D, it's done by Fateev-Zamolodchikov and Fateev-Lukyanov. Their forms are quite useful because it can be readily implemented in a computer algebra system. I just want to perform a few stupid calculation inside W-algebra of type E6, but I first need to realize it inside computer. | |
| Oct 26, 2011 at 2:51 | history | answered | Alexander Braverman | CC BY-SA 3.0 |