Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
Jean-Christophe Novelli
- Fonction : Auteur
- PersonId : 1286032
- IdRef : 050202596
Jean-Yves Thibon
- Fonction : Auteur
- PersonId : 4928
- IdHAL : jean-yves-thibon
- ORCID : 0000-0002-8976-4044
- IdRef : 033276498
Résumé
We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages induced by diffusion processes on the real line. We give several interpretations and proofs of the main result in terms of noncommutative symmetric and quasisymmetric functions, as well as generalizations involving matrix quasi-symmetric functions. The interpretation of noncommutative symmetric functions as alien operators in resurgence theory is also discussed, and a new family of Lie idempotents of descent algebras is derived from this interpretation.
Domaines
Combinatoire [math.CO]Format du dépôt | Notice |
---|---|
Type de dépôt | Article dans une revue |
Titre |
en
Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
|
Résumé |
en
We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages induced by diffusion processes on the real line. We give several interpretations and proofs of the main result in terms of noncommutative symmetric and quasisymmetric functions, as well as generalizations involving matrix quasi-symmetric functions. The interpretation of noncommutative symmetric functions as alien operators in resurgence theory is also discussed, and a new family of Lie idempotents of descent algebras is derived from this interpretation.
|
Auteur(s) |
Frédéric Menous
1
, Jean-Christophe Novelli
2
, Jean-Yves Thibon
2
1
Département de Mathématiques-Université de Paris XI
( 116202 )
- France
2
LIGM -
Laboratoire d'Informatique Gaspard-Monge
( 3210 )
- Université de Paris-Est Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2
- France
|
Comité de lecture |
Oui
|
Vulgarisation |
Non
|
Langue du document |
Anglais
|
Nom de la revue |
|
Date de production/écriture |
2012-07-10
|
Audience |
Internationale
|
Date de publication |
2013-03-22
|
Volume |
51
|
Numéro |
2
|
Page/Identifiant |
177-227
|
Domaine(s) |
|
arXiv Id | 1109.1634 |
DOI | 10.1016/j.aam.2013.02.003 |
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