Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra

DOI10.1017/S0308210500023933zbMath0698.20026MaRDI QIDQ3475469

David P. Carlisle, Grant Walker

Publication date: 1989

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

irreducible representationshighest weightssymmetric algebraSteinberg representation

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Stable homotopy theory, spectra (55P42)

Related Items (8)

Wilson spaces and stable splittings of BT^r ⋮ Truncated symmetric powers and modular representations of GL_n ⋮ Modular representations of \(\text{GL}(3,\mathbb{F}_p)\), symmetric squares, and mod-\(p\) cohomology of \(\text{GL}(3,\mathbb{Z})\) ⋮ The composition factors of \(F_ p[x_ 1, x_ 2, x_ 3\) as a \(GL(3, p)\)-module] ⋮ The \(\text{GL}_n(q)\)-module structure of the symmetric algebra around the Steinberg module. ⋮ The combinatorics of Steenrod operations on the cohomology of Grassmannians ⋮ Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients ⋮ Linking first occurrence polynomials over \( \mathbb F_p\) by Steenrod operations

Cites Work

• Subalgebras of Steenrod algebra and the action of matrices on truncated polynomial algebras
• Stable splittings derived from the Steinberg module
• Modular representations of \(GL(n,p)\), splitting \(\Sigma(CP^{\infty} \times \dots \times CP^{\infty})\) and the \(\beta\)-family as framed hypersurfaces
• Finite complexes with A(n)-free cohomology
• On the iterated complex transfer
• Stable decompositions of classifying spaces of finite abelianp-groups

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