\(p\)-filtrations and the Steinberg module

DOI10.1006/jabr.2000.8745zbMath0989.20033OpenAlexW1992576385MaRDI QIDQ5952414

Henning Haahr Andersen

Publication date: 15 April 2002

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

Full work available at URL: https://doi.org/10.1006/jabr.2000.8745

zbMATH Keywords

simple moduleshighest weightsinduced modulesconnected reductive algebraic groupsgood \(p\)-filtrationsSteinberg modules

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05)

Related Items (15)

BGG categories in prime characteristics ⋮ Reduced standard modules and cohomology ⋮ Good \(l\)-filtrations for \(q\)-\(\mathrm{GL}_3(k)\) ⋮ On Donkin’s tilting module conjecture I: lowering the prime ⋮ Decomposition of tensor products involving a Steinberg module ⋮ On (𝑝,𝑟)-filtrations and tilting modules ⋮ Metabelian Lie powers of the natural module for a general linear group ⋮ Counterexamples to the tilting and \((p,r)\)-filtration conjectures ⋮ On tensoring with the Steinberg representation ⋮ On good \((p,r)\)-filtrations for rational \(G\)-modules. ⋮ Connectedness of cup products for polynomial representations of \(\mathrm{GL}_n\) and applications ⋮ On p -filtrations of Weyl modules ⋮ A note on the tensor product of restricted simple modules for algebraic groups. ⋮ Homomorphisms between Weyl modules for $\operatorname {SL}_3(k)$ ⋮ \(p\)-filtrations of dual Weyl modules

Cites Work

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• The Frobenius morphism on the cohomology of homogeneous vector bundles on G/B
• A filtration for rational modules
• Tensor products of quantized tilting modules
• On tilting modules for algebraic groups
• Fusion categories arising from semisimple Lie algebras
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Representations of quantum algebras
• Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
• Filtrations of $G$-modules
• Representations of quantum algebras. The mixed case.
• Introduction to quantum groups

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