On extensions of simple modules over symmetric and algebraic groups

zbMath0981.20006MaRDI QIDQ1965267

Alexander S. Kleshchev, J. K. Sheth

Publication date: 20 November 2001

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

zbMATH Keywords

partitionsweightsSpecht modulessymmetric groupsextensionsWeyl modulessimple modulesconnected reductive algebraic groups

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Cohomology of groups (20J06) Cohomology theory for linear algebraic groups (20G10)

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Weyl modules and the mod 2 Steenrod algebra, Row and column removal theorems for homomorphisms of Specht modules and Weyl modules., A row removal theorem for the Ext¹ quiver of symmetric groups and Schur algebras, The blob algebra in positive characteristic., On the structure of Specht modules in the principal block of \(F\Sigma_{3p}\), The submodule structure of Specht modules., Irreducible tensor products for alternating groups in characteristics 2 and 3, First cohomology for finite groups of Lie type: Simple modules with small dominant weights, Invariant forms on irreducible modules of simple algebraic groups, Second cohomology for finite groups of Lie type., Some simple modules for classical groups and \(p\)-ranks of orthogonal and Hermitian geometries., On the cohomology of Young modules for the symmetric group., Computations and applications of some homological constants for polynomial representations of 𝐺𝐿_{𝑛}, On self-extensions of irreducible modules over symmetric groups, On Schur algebras, Ringel duality and symmetric groups.

Cites Work

• The submodule lattice of Weyl modules for symplectic groups with fundamental highest weights
• A characteristic free approach to invariant theory
• The representation theory of the symmetric groups
• Extensions of modules over Schur algebras, symmetric groups and Hecke algebras.
• On cohomology of dual Specht modules
• On the Representation Theory of the Symmetric Groups
• On the ordinary quiver of the symmetric group over a field of characteristic 2
• On Translation Functors for General Linear and Symmetric Groups
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