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- W2359327614 abstract "Let G and G' be connected linear algebraic groups over k,an algebracally closed field,G→G' an algebraic group homomorphism.Let P be a parabolic subgroup of G, and P'(P)that of G'.Thus,induces a variety morphismG/G→G'/P'。 Let E be a rational P'-module.A P-module structure,denoted by 'E,is defined on E via .Now E induces a sheaf _(G'/P')(E)on G'/P',and E induces _(G/P)(E) on G/P.The aim of this paper is to explore the connection between these induced sheaves and the connection between their cohomology groups We mainly prove: (1)There is an _(G_/p)-module isomorphism (2)Ifis an isomorphism,then there is a G-module isomorphism H~i The second couclusion is a generalization of Cline-Parshall-Scott's result[3,§1, Prop.]and the author's result[8,(2.9)]. As applications the celebrated Kempf's Vanishing Theorem is generalized to arb- itrary connected groups,and a short proof of a result of Donkin[4]is given." @default.
- W2359327614 created "2016-06-24" @default.
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- W2359327614 date "1984-01-01" @default.
- W2359327614 modified "2023-09-25" @default.
- W2359327614 title "The Inverse Image of an Induced Sheaf on G/P" @default.
- W2359327614 hasPublicationYear "1984" @default.
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