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The first cohomology group of a line bundle on G/B. (English) Zbl 0417.20038


MSC:

20G10 Cohomology theory for linear algebraic groups
20G05 Representation theory for linear algebraic groups
20G15 Linear algebraic groups over arbitrary fields
14L35 Classical groups (algebro-geometric aspects)
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References:

[1] Andersen, H.H.: On Schubert varieties inG/B and Bott’s theorem, Thesis, M.I.T., 1977
[2] Andersen, H.H.: Cohomology of line bundles onG/B, to appear in Ann. Scients. Ec. Norm. Sup.
[3] Carter, R. and Cline, E.: The submodule structure of Weyl modules for groups of typeA 1, Proc. Conf. Finite groups, pp. 303-311, Academic Press, NY, 1976 · Zbl 0356.20048
[4] Cline, E., Parshall, B and Scott, L.: Induced modules and affine quotients. Math. Ann.230, 1-14 (1977) · Zbl 0378.20033
[5] Demazure, M.: A very simple proof of Bott’s theorem, Invent. Math.,33, 271-272 (1976) · Zbl 0383.14017
[6] Green, J.A.: Locally finite representations, J. Alg.41, 137-171 (1976) · Zbl 0369.16008
[7] Griffith, W.L. Jr.: Cohomology of line bundles in characteristicp, to appear
[8] Grothendieck, A.: Sur Quelques points d’algèbre homologique, Tôhoku Math. J.9, 119-221 (1957) · Zbl 0118.26104
[9] Humphreys, J.E.: Ordinary and modular representations of Chevalley groups, Lect. Notes in Math., No. 528, 1976 · Zbl 0341.20037
[10] Kempf, G.: Linear systems on homogeneous spaces, Ann. Math.,103, 557-591 (1976) · Zbl 0327.14016
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