Generic Cartan invariants for Frobenius kernels and Chevalley groups

DOI10.1016/0021-8693(89)90221-4zbMath0674.20023OpenAlexW2035170866MaRDI QIDQ1121386

James E. Humphreys

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0021-8693(89)90221-4

zbMATH Keywords

group of rational pointsfinite groups of Lie typeaffine Weyl groupcomposition factorsCartan invariantsinjective hullcharacter groupCoxeter numbergroup schemeprojective covermaximal torusdominant weightsG-modulefundamental dominant weightssemisimple, simply connected algebraic group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Group schemes (14L15)

Related Items (5)

Loewy series for principal series representations of finite Chevalley groups ⋮ Gelfand-Kirillov dimension and mod \(p\) cohomology for \(\mathrm{GL}_2 \) ⋮ Highest weight modules for algebraic groups arising from quantum groups ⋮ Generic patterns for extensions of simple modules for finite Chevalley groups ⋮ Reduction modulo \(p\) of some Deligne-Lusztig characters

Cites Work

• Generic Cartan invariants for Chevalley groups
• Projective characters for finite Chevalley groups
• Zur Reduktion modulo p der Charaktere von Deligne und Lusztig
• Über das Dekompositionsverhalten gewisser modularer Darstellungen halbeinfacher Gruppen und ihrer Lie-Algebren
• Über Darstellungen höherer Frobenius-Kerne halbeinfacher algebraischer Gruppen
• Cartan Invariants
• Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
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