Bounding Ext for modules for algebraic groups, finite groups and quantum groups.

DOI10.1016/j.aim.2010.09.021zbMath1234.20056arXiv0909.5207OpenAlexW2124757807MaRDI QIDQ624316

Leonard L. Scott, Brian J. Parshall

Publication date: 9 February 2011

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

Full work available at URL: https://arxiv.org/abs/0909.5207

zbMATH Keywords

tilting modulesquantum groupsExtreductive algebraic groupsfinite groups of Lie typeKazhdan-Lusztig polynomialsgeneric cohomologyDonkin conjecture on projective indecomposables

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Quantum groups (quantized function algebras) and their representations (20G42) Representations of finite groups of Lie type (20C33) Cohomology theory for linear algebraic groups (20G10)

Related Items (16)

On character formulas for simple and tilting modules ⋮ Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings ⋮ Unbounding Ext. ⋮ First cohomology groups of Chevalley groups in cross characteristic. ⋮ Bounding and unbounding higher extensions for \(\mathrm{SL}_2\). ⋮ Variations on a theme of Cline and Donkin. ⋮ On the cohomology of SL₂ with coefficients in a simple module ⋮ On liftings of projective indecomposable \(G_{(1)}\)-modules ⋮ First cohomology groups for finite groups of Lie type in defining characteristic ⋮ First cohomology for finite groups of Lie type: Simple modules with small dominant weights ⋮ Cohomological growth rates and Kazhdan-Lusztig polynomials. ⋮ Cohomology of SL₂ and related structures ⋮ Bounds on the dimension of \(\mathrm{Ext}\) for finite groups of Lie type ⋮ Shifted generic cohomology ⋮ Bounding the Dimensions of Rational Cohomology Groups ⋮ Bounding cohomology for finite groups and Frobenius kernels.

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