Séminaire Lotharingien de Combinatoire, 91B.13 (2024), 12 pp.

Marcelo Aguiar, Sarah Brauner and Vic Reiner

Configuration Spaces and Peak Representations

Abstract. Eulerian idempotents of types A and B generate representations with topological interpretations, as the cohomology of configuration spaces of types A and B. We provide an analogous cohomological interpretation for the representations generated by idempotents in the peak algebra, called the peak representations. We describe the peak representations as sums of Thrall's higher Lie characters, give Hilbert series and branching rule recursions for them, and discuss connections to Jordan algebras.


Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

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