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References
[A 1] Andersen, H.H.: Vanishing theorem and induced representations, J. Algebra62, 86–100 (1980)
[A 2] Andersen, H.H.: The strong linkage principle. J. Reine Angew. Math.315, 53–59 (1980).
[A 3] Andersen, H.H.: Filtrations of cohomology modules for Chevalley groups. Ann. Sci. Éc. Norm. Super.16, 495–528 (1983)
[A 4] Andersen, H.H.: Schubert varieties and Demazure's character formula, Invent. Math.79 611–618, (1985)
[A 5] Andersen, H.H.: The linkage principle and the sum furmula for quantum groups. (Preprint)
[CPS 1] Cline, E., Parshall, B., Scott, L.: Induced modules and extensions of representations. Invent. Math.47, 41–51 (1978)
[CPS 2] Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras and representations. J. Algebra63, 98–123 (1980)
[De 1] Demazure, M.: Désingularisation des variétés de Schubert généralisées. Ann. Sci. Éc. Norm. Super.7, 53–88 (1974)
[De 2] Demazure, M.: A very simple proof of Bott's theorem. Invent. Math.33, 271–272 (1976)
[DL] Dyer, M., Lusztig, G.: Appendix to [L 6], In Geom. Ded. (1990) (to appear)
[Do] Donkin, S.: Rational representations of algebraic groups (Lect. Notes Math. vol. 1140), Berlin Heidelberg New York: Springer 1985
[Dr] Drinfeld, V.: Hopf algebras and the quantum Yang-Baxter equation. Sov. Math. Dokl.32, 254–258 (1985)
[Ja 1] Jantzen, J.C.: Darstellungen halbeinfacher Gruppen und kontravariante Formen. J. Reine Angew. Math.290, 117–141 (1977)
[Ja 2] Jantzen, J.C.: Weyl modules for groups of Lie type. In: Collins M. (ed.) Finite simple groups II Proc. Durham 1978, Academic Press, 1980, pp. 291–300
[Ja 3] Jantzen, J.C.: Representations of algebraic groups. Pure Appl. Math., vol.131, Academic Press, 1987
[Jo] Joseph, A.: On the Demazure character formula. Ann. Sci. Éc. Norm. Super.18, 389–419 (1985)
[Ji] Jimbo, M.: Aq-difference analogue ofU(g) and the Yang-Baxter equation. Lett. Math. Phys.10, 63–69 (1985)
[K] Kato, S.-i.: On the Kazhdan-Lusztig polynomials for affine Weyl groups. Adv. Math.55, 103–130 (1985)
[L 1] Lusztig, G.: Some problems in the representation theory of finite Chevalley groups. Proc. Symp. Pure Math.37, 313–317 (1980)
[L 2] Lusztig, G.: Quantum deformations of certain simple modules over enveloping algebras. Adv. Math.70, 237–249 (1988)
[L 3] Lusztig, G.: Modular representations and quantum groups. In: Classical groups and related topics. Contemp. Math.82, 59–77 (1989)
[L 4] Lusztig, G.: On quantum groups. J. Algebra (1990) (to appear)
[L 5] Lusztig, G.: Finite dimensional Hopf algebras arising from quantized universal enveloping algebras. J. Am. Math. Soc.3, 257–296 (1990)
[L 6] Lusztig, G.: Quantum groups at roots of 1. Geom. Ded. (1990) (to appear)
[Ma] Mathieu, O: Filtrations ofG-modules Ann. Sci. Éc. Norm. Sup. (1990) (to appear)
[Mu] Matsumura, H.: Commutative ring theory. Cambridge Studies in adv. math.8, C.U.P. (1989)
[P 1] Polo, P.: Variétés de Schubert et excellentes filtrations. Orbites unipotentes et representations, Astérisque173–174, 281–311 (1989)
[P 2] Polo, P.: Modules associés aux variétés de Schubert. C. R. Acad. Sci. Paris,308, 123–126 (1989) and to appear in the proceedings of the Bombay geometry colloquium 1989
[PW 1] Parshall, B., Wang, J.-p.: Quantum linear groupsI (preprint)
[PW 2] Parshall, B., Wang, J.-p.: Quantum linear groupsII (preprint)
[RR] Ramanan, S., Ramanathan, A.: Projective normality of flag varieties and Schubert varieties. Invent. Math.79, 217–224 (1985)
[R 1] Rosso, M.: Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra. Comm. Math. Phys.117, 581–593 (1988)
[R 2] Rosso, M.: Analogues de la forme de Killing et du théorème d'Harish-Chandra pour les groupes quantiques. Ann. Sci. Éc. Norm. Super.23 (1990)
[S] Sullivan, J.B.: Simply connected groups, the hyperalgebra, and Verma's conjecture. Am. J. Math.100, 1015–1019 (1977)
[W] Wang, J.-p.: Sheaf cohomology ofG/B and tensor products of Weyl modules. J. Algebra77, 162–185 (1982)
[X] Xi, N.: Finite dimensional modules of some quantum groups overF p(v). Academia Sinica (Preprint)
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Dedicated to Prof. Cao Xihua on his 70th birthday
Oblatum 17-IV-1990 & 21-VI-1990
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Andersen, H.H., Polo, P. & Kexin, W. Representations of quantum algebras. Invent. math. 104, 1–59 (1991). https://doi.org/10.1007/BF01245066
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DOI: https://doi.org/10.1007/BF01245066