A filtration for rational modules

DOI10.1007/BF01214334zbMath0455.20029WikidataQ106323576 ScholiaQ106323576MaRDI QIDQ1150044

Stephen Donkin

Publication date: 1981

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173042

zbMATH Keywords

filtration of submodulesrationally injective indecomposable modulesrepresentation of Borel subgroupsemisimple, simply connected affine algebraic group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05)

Related Items (36)

Rings of invariants of \(2\times 2\) matrices in positive characteristic ⋮ On Schur algebras and related algebras. I ⋮ Filtrations of $G$-modules ⋮ On Schur algebras and related algebras. V: Some quasi-hereditary algebras of finite type ⋮ The Frobenius morphism in invariant theory ⋮ Schur algebras and global bases: New proofs of old vanishing theorems ⋮ Ringel duality as an instance of Koszul duality ⋮ Locally finitely presented additive categories ⋮ Algebraic stratification in representation categories ⋮ On a formula of J. Deruyts ⋮ On the procedure of calculation of the invariants of an adjoint action of classical groups ⋮ Decomposition of tensor products involving a Steinberg module ⋮ On Schur algebras and related algebras III: integral representations ⋮ On the derived category of Grassmannians in arbitrary characteristic ⋮ Symmetrizers for Schur superalgebras ⋮ On minimal tilting complexes in highest weight categories ⋮ Good filtrations and strong \(F\)-regularity of the ring of \(U_P\)-invariants ⋮ On tensoring with the Steinberg representation ⋮ Pseudocompact algebras and highest weight categories ⋮ The normality of closures of conjugacy classes of matrices ⋮ On good \((p,r)\)-filtrations for rational \(G\)-modules. ⋮ Some remarks on tilting modules, double centralisers and Lie modules ⋮ Complete reducibility in good characteristic ⋮ Some remarks on the uniqueness of liftings of principal indecomposable modules for infinitesimal subgroups of semisimple groups ⋮ Combinatorics and the Schur algebra ⋮ INVARIANTS OF MIXED REPRESENTATIONS OF QUIVERS I ⋮ INVARIANTS OF MIXED REPRESENTATIONS OF QUIVERS II: DEFINING RELATIONS AND APPLICATIONS ⋮ The global dimension of Schur algebras for \(\text{GL}_2\) and \(\text{GL}_3\) ⋮ \(p\)-filtrations and the Steinberg module ⋮ Invariants of unipotent radicals ⋮ A note on the tensor product of restricted simple modules for algebraic groups. ⋮ Modules with a Demazure flag ⋮ Cohomology of induced representations for algebraic groups ⋮ A canonical filtration for certain rational modules ⋮ The Frobenius morphism in invariant theory. II ⋮ On tilting modules for algebraic groups

Cites Work

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• Cohomology of algebraic linear groups
• Category of \(\mathfrak g\) modules
• Locally finite representations
• Induced modules and affine quotients
• Über Darstellungen höherer Frobenius-Kerne halbeinfacher algebraischer Gruppen
• Rationally Injective Modules for Semisimple Algebraic Groups as Direct Limits
• Hopf Complements and Injective Comodules for Algebraic Groups
• Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
• Darstellungen halbeinfacher Gruppen und kontravariante Formen.
• Symmetry for Finite Dimensional Hopf Algebras
• Introduction to Lie Algebras and Representation Theory

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