Filtrations of G-modules
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 4, pp. 625-644.
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     author = {Mathieu, Olivier},
     title = {Filtrations of $G$-modules},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {625--644},
     publisher = {Elsevier},
     volume = {Ser. 4, 23},
     number = {4},
     year = {1990},
     doi = {10.24033/asens.1615},
     mrnumber = {92a:20044},
     zbl = {0748.20026},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1615/}
}
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Mathieu, Olivier. Filtrations of $G$-modules. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 23 (1990) no. 4, pp. 625-644. doi : 10.24033/asens.1615. http://archive.numdam.org/articles/10.24033/asens.1615/

[A1] H. H. Andersen, The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B. Ann. Math., 112, 1980, pp. 113-121. | MR | Zbl

[A2] H. H. Andersen, Schubert varieties and Demazure's character formula, Invent. Math., 79, 1985, pp. 611-618. | MR | Zbl

[A3] H. H. Andersen, The strong linkage principle. J. Reine Angew Math., 315, 1980, pp. 53-59. | MR | Zbl

[B] N. Bourbaki, Groupes et algèbres de Lie (ch. 7 et 8), Diffusion C.C.L.S., Paris, 1975.

[D] M. Demazure, Désingularisation des variétés de Schubert généralisées. Ann. Scient. Ec. Norm. Sup., 7, 1974, pp. 53-88. | Numdam | MR | Zbl

[D1] S. Donkin, Rational representations of algebraic groups. Springer Verlag, Lect. Notes Math., 1140, 1985. | MR | Zbl

[D2] S. Donkin, A filtration for rational modules, Math. Z., 117, 1981, pp. 1-8. | MR | Zbl

[D3] S. Donkin, Good filtrations of rational modules for reductive groups, Proc. Symp. Pure Math. A.M.S., 177, part 1, 1987, pp. 69-80. | MR | Zbl

[D4] S. Donkin, Invariants of Unipotent Radicals. Math. Z., 198, 1988, pp. 117-125. | MR | Zbl

[D5] S. Donkin, On conjugating representations and adjoint representations of semi-simple groups, Inv. Math., 91, 1988, pp. 137-145. | EuDML | MR | Zbl

[F] E. Friedlander, A canonical filtration for certain rational modules. Math. Z, 188, 1985, pp. 433-438. | EuDML | MR | Zbl

[H] W. Haboush, A short proof of the Kempf vanishing theorem. Invent. Math., 56, 1980, pp. 109-112. | EuDML | MR | Zbl

[H1] J. Humphreys, Ordinary and modular representations of Chevalley groups II, unpublished, 1977.

[H2] J. Humphreys, Linear algebraic groups, G.T.M.21, Springer-Verlag, Berlin, 1975. | MR | Zbl

[J1] J. Jantzen, Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne. J. Reine Angew. Math., 290, 1980, pp. 157-199. | EuDML | MR | Zbl

[J2] J. Jantzen, Representations of algebraic groups, Academic Press, Orlando, 1987. | MR | Zbl

[J] A. Joseph, On the Demazure character formula. Ann. Scient. Ec. Norm. Sup., 18, 1985, pp. 389-419. | EuDML | Numdam | MR | Zbl

[Ke] G. Kdmpf, Linear systems on homogeneous spaces, Ann. Math., 103, 1980, pp. 557-591. | MR | Zbl

[Ko] B. Kostant, Groups over ℤ. Proc. Symp. Pure Math. A.M.S., 9, 1966, pp. 90-98. | MR | Zbl

[Ku] S. Kumar, Proof of the Parthasaraty-Ranga-Rao-Varadarajan conjecture. Invent. Math., 93, 1988, pp. 117-130. | EuDML | MR | Zbl

[LS] V. Lakshmibai, C. S. Seshadri, Geometry of G/P-5. J. Alg., 100, 1986, pp. 462-557. | MR | Zbl

[L] P. Littelmann, A generalization of the Littlewood-Richardson rule (to appear in J. Algebra). | MR | Zbl

[M1] O. Mathieu, Construction d'un groupe de Kac-Moody et applications, Comp. Math., 69, 1989, pp. 37-60. | EuDML | Numdam | MR | Zbl

[M2] O. Mathieu, Filtrations of B-modules. Duke Math. J., 59-2, 1989, pp. 421-442. | MR | Zbl

[M3] O. Mathieu, Frobenius action on the B-cohomology, Proc. of "Infinite dimensional Lie algebras and groups" (Luminy 1988), ed. V. Kac, World Scientific, Adv. Ser. Math. Phys., 7, 1989, pp. 39-51. | MR | Zbl

[M4] O. Mathieu, Filtrations of G-modules. C. R. Acad. Sci., Paris, 309, 1989, pp. 273-276. | MR | Zbl

[MG] M. Mcgovern, On a theorem of Mathieu and Kumar (to appear).

[MR1] V. Mehta, A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. Math., 122, 1985, pp. 27-40. | MR | Zbl

[MR2] V. Mehta, A. Ramanathan, Schubert varieties in G/B × G/B. Comp. Math., 67, 1988, pp. 355-358. | EuDML | Numdam | MR | Zbl

[P1] P. Polo, Variétés de Schubert et excellentes filtrations. Proc. of "Orbites unipotentes et représentations" (Paris 1987), Astérisque (to appear). | Numdam | MR

[P2] P. Polo, Un critère cohomologique d'existence d'une filtration de Schubert. C. R. Acad. Sci., Paris, 307, 1988, pp. 791-794. | MR | Zbl

[P3] P. Polo, Modules associés aux variétés de Schubert. C. R. Acad. Sci., Paris, 308, 1989, pp. 37-60. | MR | Zbl

[RR] S. Ramanan, A. Ramanathan, Projective normality of flag varieties and Schubert varieties. Invent. Math., 79, 1985, pp. 217-224. | EuDML | MR | Zbl

[R1] A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay. Invent. Math., 80, 1985, pp. 283-294. | EuDML | MR | Zbl

[R2] A. Ramanathan, Equations defining Schubert varieties and Frobenius splitting of diagonals. Publ. I.H.E.S., 65, 1987, pp. 61-90. | EuDML | Numdam | MR | Zbl

[U] B. S. Upadhyada, Filtrations with Weyl module quotients of the principal indecomposable modules for the group SL(2, q). Comm. Alg., 7, 1979, pp. 1469-1488. | MR | Zbl

[vdK1] W. Van Der Kallen, Longest weight vectors and excellent filtrations (to appear). | MR | Zbl

[vdK2] W. Van Der Kallen, Letter to the author (June 1988).

[W] Wang Jian-Pian, Sheaf cohomology on G/B and tensor products of Weyl modules, J. Alg., 77, 1982, pp. 162-185. | MR | Zbl

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