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Twisted sequences of extensions. (English) Zbl 1476.17004

In this paper, the author studies dimensions of extension groups between Verma modules in a BGG category \(\mathcal{O}\) of a finite-dimensional semisimple Lie algebra over \(\mathbb{C}\). After providing new proofs for results that had already been proven, the author focuses on proving new results regarding the dimensions of \(\operatorname{Hom}_{\mathcal{O}}\)- and \(\mathrm{Ext}^1_{\mathcal{O}}\)-groups between Verma modules.

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B55 Homological methods in Lie (super)algebras
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References:

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