Timeline for Is there a category of representations of a simple Lie algebra on which its Weyl group naturally acts?
Current License: CC BY-SA 3.0
7 events
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| Sep 18, 2013 at 13:18 | comment | added | Ben Webster♦ | @GeordieWilliamson Depends on how you decide to grade your Gelfands. Is multiplication by q a generation earlier, or a generation later? | |
| Sep 14, 2013 at 6:39 | comment | added | Geordie Williamson | +1 for Gelfand multiplicity :) $[BGG:G] = (1+q)$? | |
| Sep 13, 2013 at 21:31 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Sep 13, 2013 at 6:58 | comment | added | Tobias Kildetoft | @JohnBaez Yes, that is the group you get an action of (I had forgotten that the twisting functors only had the braid relations when I wrote my original comment). | |
| Sep 13, 2013 at 5:18 | comment | added | John Baez | By the the 'braid group', do you mean the Artin group which has the same standard generators $s_i$ as the Weyl group (one per dot in the Dynkin diagram), and the same relations $(s_i s_j)^{m_{ij}} = 1$ for $i \ne j$, but lacking the relations $s_i^2 = 1$? I'm hoping you'll answer yes. The other 'sacrifice' you demand, working with the derived category of the principal block of category $\mathcal{O}$, is no problem for me, except someday I'd like a category with a monoidal structure. | |
| Sep 13, 2013 at 0:06 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Sep 12, 2013 at 22:59 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |