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Results tagged with category-o
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user 135674
Questions related to the Bernstein-Gelfand-Gelfand category O and generalizations
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Questions to the proof of Lemma 9.3 in Humphreys "Representations of Semisimple Lie algebras...
Thanks to the outstanding help of LSpice I present a version of more detailed proof of the two parts above. Do not hesitate to point out mistakes.
"$(1) \Rightarrow (2)$": Fix $\alpha \in I$ and $\mu …
- 473
1
vote
Computing kernel in the category $\mathcal{O}$
So far I only found the following messy proof. In case I did a mistake or you know a more elegant way it would be a pleasure to know. It seems to me that can be generalised to any "BGG square". Theref …
- 473
1
vote
Morphism of Verma modules
For part 2:
With
\begin{equation*}
y_{\alpha_1}=\begin{pmatrix} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix},y_{\alpha_2}=\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{pmatrix},y_{\al …
- 473