Irreducibility in algebraic groups and regular unipotent elements

DOI10.1090/S0002-9939-2012-11898-2zbMath1269.20040MaRDI QIDQ4911541

Donna M. Testerman, Alexander E. Zalesskij

Publication date: 19 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

connected reductive groupssimple algebraic groupsregular unipotent elementsSerre completely irreducible subgroups

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Structure theory for linear algebraic groups (20G07)

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Cites Work

• Nilpotent centralizers and Springer isomorphisms.
• Subgroups of type \(A_1\) containing a fixed unipotent element in an algebraic group
• \(A_ 1\)-type overgroups of elements of order \(p\) in semisimple algebraic groups and the associated finite groups
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• On the modular characters of groups
• The maximal subgroups of classical algebraic groups
• Irreducible subgroups of exceptional algebraic groups
• Maximal subgroups of exceptional algebraic groups
• Subgroups of Algebraic Groups Containing Regular Unipotent Elements
• Dimensional Criteria for Semisimplicity of Representations
• The maximal subgroups of positive dimension in exceptional algebraic groups
• Irreducible Representations of Simple Algebraic Groups Containing Matrices with Big Jordan Blocks
• Reductive subgroups of exceptional algebraic groups
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