Completely reducible $\operatorname{SL}(2)$-homomorphisms

DOI10.1090/S0002-9947-07-04289-4zbMath1128.20036arXivmath/0510377OpenAlexW1970665890MaRDI QIDQ3443141

George J. McNinch, Donna M. Testerman

Publication date: 31 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0510377

zbMATH Keywords

semisimple groupscocharactersFrobenius twistsgeometrically completely reducible imagesgroup scheme homomorphismsoptimal homomorphismstwisted-product homomorphisms

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Lie algebras of linear algebraic groups (17B45)

Related Items (10)

Some good-filtration subgroups of simple algebraic groups. ⋮ Integral exotic sheaves and the modular Lusztig–Vogan bijection ⋮ Co-𝑡-structures on derived categories of coherent sheaves and the cohomology of tilting modules ⋮ The Centralizer of a Nilpotent Section ⋮ Complete reducibility and commuting subgroups ⋮ Complete reducibility and separability ⋮ Central subalgebras of the centralizer of a nilpotent element ⋮ Nilpotent centralizers and Springer isomorphisms. ⋮ Nilpotent elements and reductive subgroups over a local field ⋮ On the smoothness of centralizers in reductive groups

Cites Work

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• Completely reducible Lie subalgebras
• Jordan algebras and algebraic groups.
• Sub-principal homomorphisms in positive characteristic.
• Unipotent elements, tilting modules, and saturation.
• Variations on a theme of Steinberg.
• Nilpotent orbits over ground fields of good characteristic
• Optimal \(\text{SL}(2)\)-homomorphisms.
• A geometric approach to complete reducibility.

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