Cohomology of G/B in characteristic p

DOI10.1016/0001-8708(86)90050-2zbMath0612.20023OpenAlexW2060995955MaRDI QIDQ1087994

James E. Humphreys

Publication date: 1986

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(86)90050-2

zbMATH Keywords

representation theoryBorel subgroupsemisimple algebraic groupcohomology of line bundles

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Classical groups (algebro-geometric aspects) (14L35) Cohomology theory for linear algebraic groups (20G10)

Related Items (10)

An inversion formula for the Kazhdan-Lusztig polynomials for affine Weyl groups ⋮ Character formulas and Frobenius subgroups of algebraic groups ⋮ Representation theory via cohomology of line bundles ⋮ On sheaf cohomology for supergroups arising from simple classical Lie superalgebras ⋮ Socle series of cohomology groups of line bundles on \(G/B\) ⋮ Extensions between simple modules for Frobenius kernels ⋮ Filtrations of cohomology modules for Chevalley groups ⋮ Another characterization of parabolic subgroups ⋮ Cohomology of line bundles on G/B for the exceptional group \(G_ 2\) ⋮ A note on the characters of the cohomology of induced vector bundles on \(G\)/\(B\) in characteristic \(p\).

Cites Work

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• Cohomology of flag varieties in characteristic p
• The first cohomology group of a line bundle on G/B
• The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B
• A short proof of the Kempf vanishing theorem
• Vanishing theorems and induced representations
• Hecke algebras and Jantzen's generic decomposition patterns
• On the structure of the cohomology of line bundles on G/B
• Representations of Coxeter groups and Hecke algebras
• The geometry of algebraic groups
• Linear systems on homogeneous spaces
• Rational and generic cohomology
• A very simple proof of Bott's theorem
• Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren
• Zur Charakterformel gewisser Darstellungen halbeinfacher Gruppen und Lie-Algebren
• Cohomology of line bundles on $G/B$
• The strong linkage principle.
• Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
• Geometry of 𝐺/𝑃
• Representations of algebraic groups in prime characteristics
• Towards the Kazhdan-Lusztig conjecture
• On Ext¹ for semisimple groups and infinitesimal subgroups
• Désingularisation des variétés de Schubert généralisées
• Darstellungen halbeinfacher Gruppen und kontravariante Formen.
• On the structure of Weyl modules

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