On configuration spaces and Whitehouse's lifts of the Eulerian representations

DOI10.1016/j.jpaa.2019.02.002zbMath1416.05293arXiv1808.04007OpenAlexW2886430294WikidataQ128310711 ScholiaQ128310711MaRDI QIDQ2001409

Victor Reiner, Nicholas Early

Publication date: 3 July 2019

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04007

zbMATH Keywords

canonical blade basisHoneycomb tessellations

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Discriminantal varieties and configuration spaces in algebraic topology (55R80)

Related Items (8)

From weakly separated collections to matroid subdivisions ⋮ Smoothly splitting amplitudes and semi-locality ⋮ Eulerian representations for real reflection groups ⋮ A type \(B\) analog of the Whitehouse representation ⋮ \({\Delta}\)-algebra and scattering amplitudes ⋮ Trimming the permutahedron to extend the parking space ⋮ Eulerian representations for real reflection groups ⋮ A type \(B\) analog of the Whitehouse representation

Cites Work

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• The Eulerian representations of \(\Sigma_ n\) as restrictions of representations of \(\Sigma_{n+1}\)
• The action of \(S_ n\) on the components of the Hodge decomposition of Hochschild homology
• Symmetric group actions on the cohomology of configurations in \(\mathbb R^d\).
• A Hodge-type decomposition for commutative algebra cohomology
• The homology of iterated loop spaces
• Homotopy of non-modular partitions and the Whitehouse module
• Non-broken circuits of reflection groups and factorization in \(D_ n\)
• Hidden \(\Sigma_{n+1}\)-actions
• The tree representation of \(\Sigma_{n+1}\)
• Harrison homology, Hochschild homology and triples
• Group actions on arrangements of linear subspaces and applications to configuration spaces
• Commutative algebras for arrangements
• The Orlik-Terao Algebra and the Cohomology of Configuration Space

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