Nonzero infinitesimal blocks of category \({\mathcal{O}}_{S}\) (Q434426)
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scientific article; zbMATH DE number 6054171
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonzero infinitesimal blocks of category \({\mathcal{O}}_{S}\) |
scientific article; zbMATH DE number 6054171 |
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Nonzero infinitesimal blocks of category \({\mathcal{O}}_{S}\) (English)
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10 July 2012
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In this paper the author gives combinatorial criteria which determine when a given singular block in the parabolic version of the BGG category \(\mathcal{O}\) associated to a simple complex finite dimensional Lie algebra \(\mathfrak{g}\) is nonzero. The answer is given in terms of the usual partial order on nilpotent orbits of \(\mathfrak{g}\).
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parabolic category \(\mathcal{O}\)
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representation type
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Verma module
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nilpotent orbit
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singular block
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