Projective modules in the category ${\scr O}_ S$: self-duality
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- by Ronald S. Irving
- Trans. Amer. Math. Soc. 291 (1985), 701-732
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800259-9
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Abstract:
Given a parabolic subalgebra ${\mathfrak {p}_S}$ of a complex, semisimple Lie algebra $\mathfrak {g}$, there is a naturally defined category ${\mathcal {O}_S}$ of $\mathfrak {g}$-modules which includes all the $\mathfrak {g}$-modules induced from finite-dimensional ${\mathfrak {p}_S}$-modules. This paper treats the question of whether certain projective modules in ${\mathcal {O}_S}$ are isomorphic to their dual modules. The projectives in question are the projective covers of those simple modules occurring in the socles of generalized Verma modules. Their self-duality is proved in a number of cases, and additional information is obtained on the generalized Verma modules.References
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Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 291 (1985), 701-732
- MSC: Primary 17B10; Secondary 22E47
- DOI: https://doi.org/10.1090/S0002-9947-1985-0800259-9
- MathSciNet review: 800259