New results on the peak algebra.

DOI10.1007/s10801-006-6922-8zbMath1107.20009arXivmath/0406418OpenAlexW2089957481MaRDI QIDQ2494268

Kathryn L. Nyman, Marcelo Aguiar, Rosa C. Orellana

Publication date: 26 June 2006

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406418

zbMATH Keywords

tensor algebrasJacobson radicalfree Lie algebrassigned permutationslinear basesEulerian idempotentspeak algebrassymmetric group algebrasSolomon descent algebras

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Ordinary representations and characters (20C15) Representations of finite symmetric groups (20C30) Group rings of finite groups and their modules (group-theoretic aspects) (20C05)

Related Items (10)

Peaks on Graphs ⋮ Enriched \(P\)-partitions and peak algebras ⋮ Representation theory of the higher-order peak algebras ⋮ Floodings of metric graphs ⋮ Equidistribution of set-valued statistics on standard Young tableaux and transversals ⋮ Further refinements of Wilf-equivalence for patterns of length 4 ⋮ The pinnacle set of a permutation ⋮ Subalgebras of Solomon's descent algebra based on alternating runs ⋮ Coloured peak algebras and Hopf algebras. ⋮ Sorting permutations with fixed pinnacle set

Uses Software

• OEIS

Cites Work

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• The peak algebra and the Hecke-Clifford algebras at \(q=0\)
• A decomposition of Solomon's descent algebra
• A decomposition of the descent algebra of the hyperoctahedral group. I, II
• Orthogonal idempotents in the descent algebra of \(B_ n\) and applications
• A Mackey formula in the group of a Coxeter group. With an appendix by J. Tits: Two properties of Coxeter complexes
• An on-line version of ``The Encyclopedia of Integer Sequences
• Shifted quasi-symmetric functions and the Hopf algebra of peak functions
• The peak algebra of the symmetric group
• The peak algebra of the symmetric group revisited.
• Duality between quasi-symmetric functions and the Solomon descent algebra
• Noncommutative Symmetric Functions II: Transformations of Alphabets
• The peak algebra and the descent algebras of types B and D
• Enriched 𝑃-Partitions

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