Document Zbl 0403.20026

On the structure of Weyl modules. (English) Zbl 0403.20026

Math. Z. 170, 1-14 (1980).

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MSC:

20G15	Linear algebraic groups over arbitrary fields
20G05	Representation theory for linear algebraic groups
20J05	Homological methods in group theory

Keywords:

Connected Reductive Algebraic Group; Filtrations of the Weyl Modules; Intertwining Homomorphisms; Top Cohomology Groups

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References:

[1]	Andersen, H.H.: Cohomology of line bundles onG/B. Ann. Sci. École Norm. Sup., Sèr. 4,12, 85-100 (1979)
[2]	Andersen, H.H.: The first cohomology group of a line bundle onG/B. Invent. Math.51, 287-296 (1979) · Zbl 0417.20038 · doi:10.1007/BF01389921
[3]	Andersen, H.H.: The strong linkage principle. J. Reine Angew. Math. (to appear) · Zbl 0439.20026
[4]	Bourbaki, N.: Groupes et Algèbres de Lie, IV?VI. Paris: Herman 1968 · Zbl 0186.33001
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[6]	Cline, E., Parshall, B., Scott, L.: Induced modules and affine quotients. Math. Ann.230, 1-14 (1977) · Zbl 0378.20033 · doi:10.1007/BF01420572
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[8]	Grothendieck, A.: Sur quelques points d’algèbre homologique. Tôhoku Math. J.9, 119-221 (1957) · Zbl 0118.26104
[9]	Jantzen, J.C.: Darstellungen halbeinfacher Gruppen und kontravariante Formen. J. Reine Angew. Math.290, 117-141 (1977) · Zbl 0342.20022 · doi:10.1515/crll.1977.290.117
[10]	Jantzen, J.C.: Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren. J. Alg.49, 1977, pp. 441-469 · Zbl 0386.20018 · doi:10.1016/0021-8693(77)90252-6
[11]	Jantzen, J.C., Humphreys, J.E.: Blocks and indecomposable modules for semisimple algebraic groups. J. Algebr.54, 494-503 (1978) · Zbl 0398.20047 · doi:10.1016/0021-8693(78)90012-1
[12]	Humphreys, J.E.: Introduction to Lie Algebras and Representation Theory. Gradnate Texts in Mathematics 9. Berlin-Heidelberg-New York: Springer 1972 · Zbl 0254.17004
[13]	Humphreys, J.E.: Ordinary and Modular Representations of Chevalley groups. Lecture Notes in Mathematics528. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0341.20037
[14]	Kempf, G.: Linear systems on homogeneous spaces. Ann. of Math.103, 557-591 (1976) · Zbl 0327.14016 · doi:10.2307/1970952

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