Higher extensions between modules for \(\text{SL}_2\).

DOI10.1016/j.aim.2006.05.015zbMath1112.20039arXivmath/0508155OpenAlexW2049202926MaRDI QIDQ864576

Alison E. Parker

Publication date: 12 February 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508155

zbMATH Keywords

cohomologyWeyl modulessimple moduleshighest weightsspecial linear groupsLyndon-Hochschild-Serre spectral sequencesext groups

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Cohomology theory for linear algebraic groups (20G10)

Related Items (16)

Reductive pairs arising from representations. ⋮ The Frobenius morphism in invariant theory ⋮ On certain tilting modules for \(\mathrm{SL}_{2}\) ⋮ A Clebsch-Gordan decomposition in positive characteristic ⋮ Unbounding Ext. ⋮ The Weyl extension algebra of \(GL_2(\overline{\mathbb F}_p)\). ⋮ Bounding and unbounding higher extensions for \(\mathrm{SL}_2\). ⋮ On the cohomology of SL₂ with coefficients in a simple module ⋮ First degree cohomology of Specht modules and extensions of symmetric powers ⋮ Universal extension classes for \(GL_2\). ⋮ Cohomology of SL₂ and related structures ⋮ The second cohomology of simple $SL_2$-modules ⋮ Cohomology and generic cohomology of Specht modules for the symmetric group. ⋮ Integral \(\mathrm{Ext}^2\) between hook Weyl modules ⋮ On extensions of hook Weyl modules ⋮ Koszul dual 2-functors and extension algebras of simple modules for \(\mathrm{GL}_2\).

Cites Work

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• Rational representations of algebraic groups: Tensor products and filtrations
• Linear algebraic groups
• Cohomology of modules in the principal block of a finite group
• Extensions of modules for \(\text{SL}(2,K)\)
• On Ext-transfer for algebraic groups.
• \(\text{Ext}^ 1\) for Weyl modules of \(\text{SL}_ 2(K)\)
• Quantum GL_n
• HOMOMORPHISMS AND HIGHER EXTENSIONS FOR SCHUR ALGEBRAS AND SYMMETRIC GROUPS
• Darstellungen halbeinfacher Gruppen und ihrer Frobenius-Kerne.
• Appendix. Some remarks on Ext groups
• On Ext² between Weyl modules for quantum GL_n
• Decomposition of tensor products of modular irreducibles for SL2
• The global dimension of Schur algebras for \(\text{GL}_2\) and \(\text{GL}_3\)

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