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On multiplicities of simple subquotients in generalized Verma modules
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 337-343 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We reduce the problem on multiplicities of simple subquotients in an $\alpha $-stratified generalized Verma module to the analogous problem for classical Verma modules.
We reduce the problem on multiplicities of simple subquotients in an $\alpha $-stratified generalized Verma module to the analogous problem for classical Verma modules.
Classification : 17B10, 22E47
Keywords: simple Lie algebra; Verma module; multiplicity 
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     title = {On multiplicities of simple subquotients in generalized {Verma} modules},
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Khomenko, Alexandre; Mazorchuk, Volodymyr. On multiplicities of simple subquotients in generalized Verma modules. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 2, pp. 337-343. http://geodesic.mathdoc.fr/item/CMJ_2002_52_2_a9/

[1] J. L. Brylinski and M. Kashiwara: Kazhdan-Lusztig conjecture and holonomic systems. Inv. Math. 64 (1981), 387–410. | DOI | MR

[2] L. Casian and D. Collingwood: The Kazhdan-Lusztig conjecture for generalized Verma modules. Math. Z. 195 (1987), 581–600. | DOI | MR

[3] A. J. Coleman and V. M. Futorny: Stratified L-modules. J. Algebra 163 (1994), 219–234. | MR

[4] J. Dixmier: Algebres Enveloppantes. Gauthier-Villars, Paris, 1974. | MR | Zbl

[5] V. Futorny and V. Mazorchuk: Structure of $\alpha $-stratified modules for finite-dimensional Lie algebras. J. Algebra I, 183 (1996), 456–482. | DOI | MR

[6] A. Khomenko and V. Mazorchuk: Generalized Verma modules over the Lie algebra of type $G_2$. Comm. Algebra 27 (1999), 777–783. | DOI | MR

[7] O. Mathieu: Classification of irreducible weight modules. Ann. Inst. Fourier (Grenoble) 50 (2000), 537–592. | DOI | MR | Zbl

[8] V. S. Mazorchuk: The structure of an $\alpha $-stratified generalized Verma module over Lie Algebra $\mathop {\mathrm sl}(n,{\mathbb{C}})$. Manuscripta Math. 88 (1995), 59–72. | DOI | MR

[9] A. Rocha-Caridi: Splitting criteria for $G$-modules induced from a parabolic and a Bernstein-Gelfand-Gelfand resolution of a finite-dimensional, irreducible $G$-module. Trans. Amer. Math. Soc. 262 (1980), 335–366. | MR