Timeline for Around the socle filtration of a Verma module
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2013 at 20:14 | comment | added | Reladenine Vakalwe | I agree with the type $A_2$ check (although I don't think I could typeset the lattice/diagram). Stroppel's diagram is pretty impressive! I am reasonably sure that b) is true in general (since I believe Mazorchuk's result), but of course I don't understand why. | |
| Jan 6, 2013 at 19:43 | comment | added | Dag Oskar Madsen | I am now talking about (b) of course. | |
| Jan 6, 2013 at 19:42 | comment | added | Dag Oskar Madsen | It holds in type $A_1 \times A_1$ and also in type $A_2$ as far as I can see? There is an impressive diagram of $\Delta_{w_0}$ in type $A_3$ on page 344 of [Stroppel, Catharina. Category $\scr O$: quivers and endomorphism rings of projectives. Represent. Theory 7 (2003), 322--345 (electronic)], but maybe this is the point where one realises it is time to look for more conceptual reasons it should hold or not :) | |
| Jan 6, 2013 at 19:36 | comment | added | Reladenine Vakalwe | Inspired by your example, as long as I did it correctly, c) is false in type $A_2$ also, and I am reasonably sure is essentially always going to fail (with the exception of $\mathfrak{sl}_2$). | |
| Jan 6, 2013 at 18:46 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
more suggestive notation
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| Jan 6, 2013 at 18:32 | comment | added | Reladenine Vakalwe | Yes! This is a nice counterexample. Not simple, but that's a minor quibble. Thank you! Any thoughts on b)? | |
| Jan 6, 2013 at 17:15 | history | answered | Dag Oskar Madsen | CC BY-SA 3.0 |