The Steinberg function of a finite Lie algebra

DOI10.1007/BF01390252zbMath0435.20025OpenAlexW2068842980WikidataQ115393609 ScholiaQ115393609MaRDI QIDQ1140162

T. A. Springer

Publication date: 1980

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142721

zbMATH Keywords

characteristic functionSteinberg representationnilpotent varietyfinite Lie algebranumber of nilpotent elementsreductive k-groupSteinberg function

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) Lie algebras of linear algebraic groups (17B45) Associated Lie structures for groups (20F40)

Related Items (14)

Counting symmetric nilpotent matrices ⋮ Unipotent elements in small characteristic. IV. ⋮ The Hesselink stratification of nullcones and base change. ⋮ Nilpotent classes and sheets of Lie algebras in bad characteristic ⋮ The space of invariant functions on a finite Lie algebra ⋮ Unnamed Item ⋮ Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field ⋮ Fourier transforms of nilpotently supported invariant functions on a finite simple Lie algebra ⋮ On \(\mathbb F_q\)-rational structure of nilpotent orbits in the Witt algebra ⋮ On a formula of Solomon ⋮ Nilpotent pieces in the dual of odd orthogonal Lie algebras ⋮ Unipotent elements in small characteristic. III. (With an appendix with T. Xue). ⋮ An Analogue of the Jacobson-Morozov Theorem for Lie Algebras of Reductive Groups of Good Characteristics ⋮ Nilpotent orbits in good characteristic and the Kempf-Rousseau theory

Cites Work

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• A formula for the characteristic function of the unipotent set of a finite Chevalley group
• Spherical buildings and the character of the Steinberg representation
• Instability in invariant theory
• Groupes reductifs
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• Endomorphisms of linear algebraic groups

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