A decomposition theorem for certain self-dual modules in the category 𝒪
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Duke Mathematical Journal

A decomposition theorem for certain self-dual modules in the category $\mathcal{O}$

David H. Collingwood and Ronald S. Irving

Source: Duke Math. J. Volume 58, Number 1 (1989), 89-102.

First Page PDF: View first page of article (PDF, 117 KB)

Primary Subjects: 17B10
Secondary Subjects: 17B20, 22E45, 22E47

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077307374
Mathematical Reviews number (MathSciNet): MR1016415
Zentralblatt MATH identifier: 0673.17003
Digital Object Identifier: doi:10.1215/S0012-7094-89-05806-7

References

[1] J. N. Bernstein and S. I. Gelfand, Tensor products of finite- and infinite-dimensional representations of semisimple Lie algebras, Compositio Math. 41 (1980), no. 2, 245–285.
Mathematical Reviews (MathSciNet): MR82c:17003
Zentralblatt MATH: 0445.17006
[2] T. J. Enright and B. Shelton, Decompositions in categories of highest weight modules, J. Algebra 100 (1986), no. 2, 380–402.
Mathematical Reviews (MathSciNet): MR87i:22037
Zentralblatt MATH: 0601.17005
Digital Object Identifier: doi:10.1016/0021-8693(86)90083-9
[3] R. S. Irving, Projective modules in the category ${\scr O}\sb S$: self-duality, Trans. Amer. Math. Soc. 291 (1985), no. 2, 701–732.
Mathematical Reviews (MathSciNet): MR87i:17005
Zentralblatt MATH: 0594.17005
Digital Object Identifier: doi:10.2307/2000106
[4] R. S. Irving, A filtered category $\mathcal{O}_S$: Self-duality, preprint, 1988.
[5] A. Rocha-Caridi, Splitting criteria for ${\germ g}$-modules induced from a parabolic and the Berňsteĭn-Gelfand-Gelfand resolution of a finite-dimensional, irreducible ${\germ g}$-module, Trans. Amer. Math. Soc. 262 (1980), no. 2, 335–366.
Mathematical Reviews (MathSciNet): MR82f:17006
Zentralblatt MATH: 0449.17008
Digital Object Identifier: doi:10.2307/1999832
JSTOR: links.jstor.org

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