Abstract
We study α-stratified modules of Verma type for the Lie algebrasl(n, ℂ). Necessary and sufficient conditions are established for existence of a submodule in a generalized Verma module.
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References
I. N. Bernstein, I. M. Gelfand andS. I. Gelfand, The structure of representation generated by vector of highest weight., Functional Anal. Appl. 5, 1–9 (1971)
A. J. Coleman, V. M. Futorny, StratifiedL-modules, Mathematical Preprint #1990-15
J. Dixmier, Algebras enveloppants, Ganthier Villars, Paris, 1974
Yu. A. Drozd, S. A. Ovsienko andV. M. Futorny, S-homomorphism of Harish-Chandra and\(\mathfrak{G}\) generated by semiprimitive elements// Ukrainian Math. J. 42, 1032–1037 (1990)
S. L. Fernando, Simple weight modules of complex reductive Lie algebras., Ph. D. Thesis, Univ. of Wisconsin, 1983.
V. M. Futorny, A generalization of Verma modules and irreducible representations of the Lie algebrasl(3, ℂ)// Ukrainian Math. J. 38, 422–427 (1986)
V. M. Futorny, Weightsl(3)-modules, generated by semiprimitive element.// Ukrainian Math. J. 43, 281–285 (1991)
V. M. Futorny, The weight representation of semisimple finitedimentional Lie algebras., Ph. D. Thesis, Univ. of Kiev, 1987
J. Lepowsky, Generalized Verma modules, the Cartan-Helgason theorem and the Harish-Chandra isomorphism., J. Algebra 49, 470–495 (1977)
V. S. Mazorchuk, α-stratified modules over Lie algebrasl(n, ℂ)// Ukrainian Math. J. 45, 1215–1224 (1993)
D. N. Verma, Structure of representation of complex semisimple Lie algebras.// Bull. Amer. Math. Soc. 74, 160–166 (1986)
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Mazorchuk, V. On the structure of an α-stratified generalized Verma module over Lie algebrasl(n, ℂ)). Manuscripta Math 88, 59–72 (1995). https://doi.org/10.1007/BF02567805
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DOI: https://doi.org/10.1007/BF02567805