The Eulerian representations of \(\Sigma_ n\) as restrictions of representations of \(\Sigma_{n+1}\)

DOI10.1016/S0022-4049(96)00014-XzbMath0870.20013MaRDI QIDQ675140

Sarah Whitehouse

Publication date: 17 July 1997

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

zbMATH Keywords

group algebrassymmetric groupsrepresentationsHochschild homologycharacter formulaEulerian idempotentsirreduciblescyclic homology theories

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03)

Related Items

Lie idempotent algebras. ⋮ A type \(B\) analog of the Whitehouse representation ⋮ Extending the parking space ⋮ Embeddings of higher Lie modules. ⋮ Trimming the permutahedron to extend the parking space ⋮ On configuration spaces and Whitehouse's lifts of the Eulerian representations ⋮ The integral tree representation of the symmetric group ⋮ A type \(B\) analog of the Whitehouse representation ⋮ Affine shuffles, shuffles with cuts, the Whitehouse module, and patience sorting

Cites Work

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• The action of \(S_ n\) on the components of the Hodge decomposition of Hochschild homology
• A decomposition for the cyclic cohomology of a commutative algebra
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• On the action of the symmetric group on the cohomology of the complement of its reflecting hyperplanes
• On the eigenvalues of representations of reflection groups and wreath products
• A Hodge-type decomposition for commutative algebra cohomology
• Some aspects of groups acting on finite posets
• The tree representation of \(\Sigma_{n+1}\)