Timeline for Kazhdan-Lusztig theorem for composition factors of Verma modules
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2017 at 11:12 | vote | accept | Antoine | ||
| Aug 3, 2017 at 11:09 | comment | added | Antoine | Thank you for the useful comments, I agree that I adapted somewhat the notations to formulate my question, and maybe I altered the correctness of the textbook (about which I have no doubt !). I was aware that the answer should be found in the translation functors of chapter 7, but I confess I only read it superficially (I don't have much background in category theory), and didn't find the relevant statement. | |
| Aug 3, 2017 at 11:04 | history | edited | Antoine | CC BY-SA 3.0 |
typo M_x
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| Aug 2, 2017 at 17:28 | comment | added | Jim Humphreys | P.S. A small typographical correction: it's $M_x$ rather than $M_w$ in the formula. | |
| Aug 2, 2017 at 17:12 | comment | added | Jim Humphreys | Actually, the notations aren't quite what I used in 8.4, since (as in the 1979 paper of Kazhdan-Lusztig) I emphasized the principal block (block containing the trivial module) for which $M_w, L_x$ are shorthand labels. Aside from that, the idea is to use Jantzen's translation functors between regular blocks, while translating into upper closures of Weyl chambers to get singular weights. See my Chapter 7 and also the details in 8.8. Though Chapter 8 is only a "survey", I tried to state things correctly. See my AMS bookpage or my homepage for corrections and let me know of others. | |
| Aug 2, 2017 at 15:56 | answer | added | Ben Webster♦ | timeline score: 4 | |
| Aug 2, 2017 at 15:00 | comment | added | dhy | If I understand your question correctly, the answer is yes (apply a translation functor to reduce the case of general integral antidominant $\lambda$ to any individual such weight.) | |
| Aug 2, 2017 at 14:56 | history | asked | Antoine | CC BY-SA 3.0 |