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Results tagged with category-o
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user 15292
Questions related to the Bernstein-Gelfand-Gelfand category O and generalizations
2
votes
Accepted
Computing kernel in the category $\mathcal{O}$
Here is a less direct, but shorter, proof using some non-trivial machinery. Denote by $s$, $t$ the simple reflections, and $M_w := M(w \cdot 0)$ where $w \in W$, and $\cdot$ is the "shifted" action $w …
- 1,368
4
votes
Accepted
BGG Category $\mathcal{O}$ is not closed under extension
You can usually extend two modules from $\mathcal{O}$ by a module which is not semisimple for the Cartan subalgebra (i.e. fails to be a weight module). See Exercise 3.1. in [J. E. Humphreys, Represent …
- 1,368