Filtrations of $G$-modules

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1. [A1] H. H. ANDERSEN, The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B. Ann. Math., 112, 1980, pp. 113-121. Zbl0421.20016MR81i:14009
2. [A2] H. H. ANDERSEN, Schubert varieties and Demazure's character formula, Invent. Math., 79, 1985, pp. 611-618. Zbl0591.14036MR86h:14042
3. [A3] H. H. ANDERSEN, The strong linkage principle. J. Reine Angew Math., 315, 1980, pp. 53-59. Zbl0439.20026MR81b:14006
4. [B] N. BOURBAKI, Groupes et algèbres de Lie (ch. 7 et 8), Diffusion C.C.L.S., Paris, 1975. 
5. [D] M. DEMAZURE, Désingularisation des variétés de Schubert généralisées. Ann. Scient. Ec. Norm. Sup., 7, 1974, pp. 53-88. Zbl0312.14009MR50 #7174
6. [D1] S. DONKIN, Rational representations of algebraic groups. Springer Verlag, Lect. Notes Math., 1140, 1985. Zbl0586.20017MR87b:20054
7. [D2] S. DONKIN, A filtration for rational modules, Math. Z., 117, 1981, pp. 1-8. Zbl0455.20029MR84e:20048
8. [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. Zbl0648.20048MR89f:20048
9. [D4] S. DONKIN, Invariants of Unipotent Radicals. Math. Z., 198, 1988, pp. 117-125. Zbl0627.14013MR89e:20076
10. [D5] S. DONKIN, On conjugating representations and adjoint representations of semi-simple groups, Inv. Math., 91, 1988, pp. 137-145. Zbl0639.20021MR89a:20047
11. [F] E. FRIEDLANDER, A canonical filtration for certain rational modules. Math. Z, 188, 1985, pp. 433-438. Zbl0535.20022MR86h:20062
12. [H] W. HABOUSH, A short proof of the Kempf vanishing theorem. Invent. Math., 56, 1980, pp. 109-112. Zbl0432.14027MR81g:14008
13. [H1] J. HUMPHREYS, Ordinary and modular representations of Chevalley groups II, unpublished, 1977. 
14. [H2] J. HUMPHREYS, Linear algebraic groups, G.T.M.21, Springer-Verlag, Berlin, 1975. Zbl0325.20039MR53 #633
15. [J1] J. JANTZEN, Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne. J. Reine Angew. Math., 290, 1980, pp. 157-199. Zbl0451.20040MR82b:20057
16. [J2] J. JANTZEN, Representations of algebraic groups, Academic Press, Orlando, 1987. Zbl0654.20039MR89c:20001
17. [J] A. JOSEPH, On the Demazure character formula. Ann. Scient. Ec. Norm. Sup., 18, 1985, pp. 389-419. Zbl0589.22014MR87g:17006a
18. [Ke] G. KDMPF, Linear systems on homogeneous spaces, Ann. Math., 103, 1980, pp. 557-591. Zbl0327.14016MR53 #13229
19. [Ko] B. KOSTANT, Groups over ℤ. Proc. Symp. Pure Math. A.M.S., 9, 1966, pp. 90-98. Zbl0199.06903MR34 #7528
20. [Ku] S. KUMAR, Proof of the Parthasaraty-Ranga-Rao-Varadarajan conjecture. Invent. Math., 93, 1988, pp. 117-130. Zbl0668.17008MR89j:17009
21. [LS] V. LAKSHMIBAI, C. S. SESHADRI, Geometry of G/P-5. J. Alg., 100, 1986, pp. 462-557. Zbl0618.14026MR87k:14059
22. [L] P. LITTELMANN, A generalization of the Littlewood-Richardson rule (to appear in J. Algebra). Zbl0704.20033
23. [M1] O. MATHIEU, Construction d'un groupe de Kac-Moody et applications, Comp. Math., 69, 1989, pp. 37-60. Zbl0678.17012MR90f:17012
24. [M2] O. MATHIEU, Filtrations of B-modules. Duke Math. J., 59-2, 1989, pp. 421-442. Zbl0721.20028MR90k:14056
25. [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. Zbl0764.17018MR91g:14049
26. [M4] O. MATHIEU, Filtrations of G-modules. C. R. Acad. Sci., Paris, 309, 1989, pp. 273-276. Zbl0705.20039MR91b:20054
27. [MG] M. MCGOVERN, On a theorem of Mathieu and Kumar (to appear). 
28. [MR1] V. MEHTA, A. RAMANATHAN, Frobenius splitting and cohomology vanishing for Schubert varieties, Ann. Math., 122, 1985, pp. 27-40. Zbl0601.14043MR86k:14038
29. [MR2] V. MEHTA, A. RAMANATHAN, Schubert varieties in G/B × G/B. Comp. Math., 67, 1988, pp. 355-358. Zbl0665.14020MR89k:14090
30. [P1] P. POLO, Variétés de Schubert et excellentes filtrations. Proc. of "Orbites unipotentes et représentations" (Paris 1987), Astérisque (to appear). Zbl0733.20021
31. [P2] P. POLO, Un critère cohomologique d'existence d'une filtration de Schubert. C. R. Acad. Sci., Paris, 307, 1988, pp. 791-794. Zbl0669.20034MR91b:20055
32. [P3] P. POLO, Modules associés aux variétés de Schubert. C. R. Acad. Sci., Paris, 308, 1989, pp. 37-60. Zbl0678.20027MR90f:20056
33. [RR] S. RAMANAN, A. RAMANATHAN, Projective normality of flag varieties and Schubert varieties. Invent. Math., 79, 1985, pp. 217-224. Zbl0553.14023MR86j:14051
34. [R1] A. RAMANATHAN, Schubert varieties are arithmetically Cohen-Macaulay. Invent. Math., 80, 1985, pp. 283-294. Zbl0541.14039MR87d:14044
35. [R2] A. RAMANATHAN, Equations defining Schubert varieties and Frobenius splitting of diagonals. Publ. I.H.E.S., 65, 1987, pp. 61-90. Zbl0634.14035MR88k:14032
36. [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. Zbl0425.20005MR80j:20045
37. [vdK1] W. VAN DER KALLEN, Longest weight vectors and excellent filtrations (to appear). Zbl0642.20037
38. [vdK2] W. VAN DER KALLEN, Letter to the author (June 1988). 
39. [W] WANG JIAN-PIAN, Sheaf cohomology on G/B and tensor products of Weyl modules, J. Alg., 77, 1982, pp. 162-185. Zbl0493.20023MR84h:20032

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