Timeline for Checking axiom of Category $\mathcal{O}$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2020 at 13:25 | vote | accept | KKD | ||
| Jun 1, 2020 at 21:40 | comment | added | Vít Tuček | Yes. If you already know that $\mathcal{O}$ is closed under quotients then this is a good argument. | |
| Jun 1, 2020 at 20:04 | comment | added | KKD | Thanks for this detailed answer. Could we argue also in the following way: $U(\mathfrak{g}) \otimes_{U(\mathfrak{b})} N$ lies in Category $\mathcal{O}$, which is closed under submodules and quotients. By the map you have given $M$ is a quotient of $U(\mathfrak{g}) \otimes_{U(\mathfrak{b})} N$ and therefore lies in category $\mathcal{O}$ too. Hence has to be locally $U(\mathfrak{b})$-finite. | |
| May 29, 2020 at 22:05 | history | answered | Vít Tuček | CC BY-SA 4.0 |