Representation theory of the higher order peak algebras
Jean-Christophe Novelli, Franco Saliola, Jean-Yves Thibon
TL;DR
This paper explores the representation theory of higher order unital peak algebras, providing new insights into their structure, including idempotents, quivers, and invariants, along with novel interpretations and generating functions.
Contribution
It introduces new interpretations and generating functions for idempotents in descent algebras, advancing understanding of higher order peak algebra representations.
Findings
Characterization of idempotents and quivers for higher order peak algebras
New formulas for Cartan invariants and Loewy series
Enhanced understanding of the algebraic structure and representations
Abstract
The representation theory (idempotents, quivers, Cartan invariants and Loewy series) of the higher order unital peak algebras is investigated. On the way, we obtain new interpretations and generating functions for the idempotents of descent algebras introduced in [F. Saliola, J. Algebra 320 (2008) 3866.]
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics