Unipotent elements of finite groups of Lie type and realization fields of their complex representations.

DOI10.1016/S0021-8693(03)00174-1zbMath1051.20008WikidataQ115340497 ScholiaQ115340497MaRDI QIDQ1421806

Alexander E. Zalesskij, Pham Hũ'u Tiêp

Publication date: 3 February 2004

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

zbMATH Keywords

finite groups of Lie typeunramified extensionsunipotent elements\(p\)-rational group charactersfinite connected reductive groupsstrongly rational classes

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Representations of finite groups of Lie type (20C33)

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Cites Work

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• Caractères unipotents de \({}^ 3D_ 4({\mathbb{F}}_ q)\)
• The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
• The conjugate classes of unipotent elements of the Chevalley groups \(E_ 7\) and \(E_ 8\).
• Classes unipotentes et sous-groupes de Borel
• On the values of characters of semi-simple groups over finite fields
• Basic sets of Brauer characters of finite groups of Lie type. III
• The Schur indices of the irreducible characters of the special linear groups
• The conjugate classes of Chevalley groups of type \((G_2)\)
• \(A_ 1\)-type overgroups of elements of order \(p\) in semisimple algebraic groups and the associated finite groups
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• A non-duality theorem for finite groups
• On the representation of \(-1\) as a sum of two-squares in an algebraic number field
• Mod p Reducibility of Unramified Representations of Finite Groups of Lie Type
• Properties of the Characters of the Finite General Linear Group Related to the Transpose-Inverse Involution
• Centralizers of Semisimple Elements in the Finite Classical Groups
• The characters of the group of rational points of a reductive group with non-connected centre.
• Remarks on Computing Irreducible Characters
• Subgroups of Algebraic Groups Containing Regular Unipotent Elements
• Reducibility modulo $p$ of complex representations of finite groups of Lie type: Asymptotical result and small characteristic cases
• Jordan block sizes of unipotent elements in exceptional algebraic groups
• On Ree's Series of Simple Groups
• The centralizer of a regular unipotent element in a semisimple algebraic group
• The Characters of the Finite Symplectic Group Sp(4,q)
• On the Overgroups of Irreducible Subgroups of the Finite Classical Groups
• On a class of doubly transitive groups