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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