The modular Hecke algebra and Steinberg representation of finite Chevalley groups (with an appendix by Peter Landrock)

DOI10.1016/0021-8693(84)90130-3zbMath0563.20015OpenAlexW1968878960MaRDI QIDQ1057361

Nicholas J. Kuhn

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90130-3

zbMATH Keywords

Hecke algebrafinite Chevalley groupsSteinberg idempotentsimple rootSteinberg representationfinite group with split (B,N) pairIwahori relations

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (11)

Embeddings of Hecke algebras in group algebras ⋮ The transfer and Whitehead's conjecture ⋮ Representations of finite groups ⋮ Minc's generating function and a ``Segal conjecture for certain Thom spectra ⋮ Generators for the mod 2 cohomology of the Steinberg summand of Thom spectra over \(B(\mathbb Z/2)^n\) ⋮ 0-Hecke algebra actions on coinvariants and flags ⋮ On decomposition of modular representations from Cohen-Macaulay geometries ⋮ On the action of the Iwahori–Hecke algebra on modular invariants ⋮ The Steinberg representation ⋮ Generators for the mod-\(p\) cohomology of the Steinberg summand of Thom spectra over \(\mathrm{B}(\mathbb{Z}/p)^n\)-odd primary cases ⋮ Un complexe de Koszul de modules instables et cohomotopie d’un spectre de Thom

Cites Work

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• Stable splittings derived from the Steinberg module
• Truncation and duality in the character ring of a finite group of Lie type
• Groups with a (B,N)-pair of rank 2. I
• Representations of finite groups of Lie type
• Prime Power Representations of Finite Linear Groups II
• A Kahn-Priddy sequence and a conjecture of G. W. Whitehead
• The Whitehead conjecture and splitting 𝐵(𝐙/2)^{𝐤}

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