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- W2019440872 abstract "On s'intéresse aux compactifications équivariantes d'un groupe réductif quelconque, G, complexe et connexe, vu comme espace homogène pour G×G. Pour un revêtement fini G̃ de G, les groupes de cohomologie des fibrés en droites sur ces compactifications sont naturellement des G̃×G̃-modules de dimension finie. On détermine, dans cet article, tous ces G̃×G̃-modules en calculant leur multiplicité selon chaque G̃×G̃-module simple. La formule obtenue est en particulier valable pour la compactification magnifique d'un groupe adjoint et généralise aussi la description bien connue de la cohomologie des fibrés en droites sur les variétés toriques complètes. Notre méthode repose sur le complexe de Grothendieck–Cousin, qui, si g est l'algèbre de Lie de G, est un complexe de g×g-modules. Pour analyser ces g×g-modules, on en donne des filtrations dont le gradué associé fait intervenir des << modules de Verma généralisés >>. We consider equivariant compactifications of some reductive complex and connected group, G, considered as an homogeneous space for G×G. For a finite covering G̃ of G, the cohomology groups of line bundles over those compactifications are naturally finite dimensional G̃×G̃-modules. We determine, in this article, all those G̃×G̃-modules by calculating their multiplicities along each simple G̃×G̃-module. The achieved formula is in particular valid for the wonderful compactification of adjoint groups and also generalizes the well known description of the cohomology of line bundles over complete toric varieties. Our method is based upon the Grothendieck–Cousin complex which, if g is the Lie algebra of G, is a g×g-module complex. We analyse those g×g-modules by giving some filtrations in the associated graduate of which, some “generalized Verma modules” occur." @default.
- W2019440872 created "2016-06-24" @default.
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- W2019440872 date "2004-05-01" @default.
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- W2019440872 title "Cohomologie des fibrés en droites sur les compactifications des groupes réductifs" @default.
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- W2019440872 doi "https://doi.org/10.1016/j.ansens.2003.11.001" @default.
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