Structure of cohomology of line bundles on G/B for semisimple groups

DOI10.1016/0021-8693(90)90220-IzbMath0732.20028MaRDI QIDQ809186

Zhengyuan Lin

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

line bundlesemi-simple algebraic groupFrobenius subgroupsLoewy seriesmodular irreducible charactersinfinitesimally induced representationssocle and radical of cohomology modules

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Representation theory for linear algebraic groups (20G05) Lie algebras of linear algebraic groups (17B45) Cohomology theory for linear algebraic groups (20G10) Modular Lie (super)algebras (17B50)

Related Items (8)

Loewy series for principal series representations of finite Chevalley groups ⋮ Representation theory via cohomology of line bundles ⋮ Socle series of cohomology groups of line bundles on \(G/B\) ⋮ Extensions between simple modules for Frobenius kernels ⋮ Highest weight modules for algebraic groups arising from quantum groups ⋮ Generic patterns for extensions of simple modules for finite Chevalley groups ⋮ A note on the characters of the cohomology of induced vector bundles on \(G\)/\(B\) in characteristic \(p\). ⋮ Structure of cohomology of line bundles on G/B for semisimple groups

Cites Work

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• The first cohomology group of a line bundle on G/B
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• Jantzen's filtrations of Weyl modules
• Filtration patterns for representations of algebraic groups and their Frobenius kernels
• On the structure of the higher cohomology modules of line bundles on G/B
• On the geometry of extensions of irreducible modules for simple algebraic groups
• Translation and cancellation of socle series patterns
• Character formulas and Frobenius subgroups of algebraic groups
• On the structure of the cohomology of line bundles on G/B
• Filtrations of cohomology modules for Chevalley groups
• On Injective Modules for Infinitesimal Algebraic Groups, I
• On the Generic Structure of Cohomology Modules for Semisimple Algebraic Groups
• The strong linkage principle.
• Loewy Series of Modules for the First Frobenius Kernel in a Reductive Algebraic Group

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