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Article

Keywords:
simple Lie algebra; Verma module; multiplicity
Summary:
We reduce the problem on multiplicities of simple subquotients in an $\alpha $-stratified generalized Verma module to the analogous problem for classical Verma modules.
References:
[1] J. L. Brylinski and M. Kashiwara: Kazhdan-Lusztig conjecture and holonomic systems. Inv. Math. 64 (1981), 387–410. DOI 10.1007/BF01389272 | MR 0632980
[2] L. Casian and D. Collingwood: The Kazhdan-Lusztig conjecture for generalized Verma modules. Math. Z. 195 (1987), 581–600. DOI 10.1007/BF01166705 | MR 0900346
[3] A. J. Coleman and V. M. Futorny: Stratified L-modules. J. Algebra 163 (1994), 219–234. MR 1257315
[4] J. Dixmier: Algebres Enveloppantes. Gauthier-Villars, Paris, 1974. MR 0498737 | Zbl 0308.17007
[5] V. Futorny and V. Mazorchuk: Structure of $\alpha $-stratified modules for finite-dimensional Lie algebras. J. Algebra I, 183 (1996), 456–482. DOI 10.1006/jabr.1996.0229 | MR 1399036
[6] A. Khomenko and V. Mazorchuk: Generalized Verma modules over the Lie algebra of type $G_2$. Comm. Algebra 27 (1999), 777–783. DOI 10.1080/00927879908826460 | MR 1671979
[7] O. Mathieu: Classification of irreducible weight modules. Ann. Inst. Fourier (Grenoble) 50 (2000), 537–592. DOI 10.5802/aif.1765 | MR 1775361 | Zbl 0962.17002
[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 10.1007/BF02567805 | MR 1348790
[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 0586721
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