Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
Copyright policy )Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras
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.
51 pages
- University of Paris-Saclay France
- École des Ponts ParisTech France
- Laboratoire de Mathématiques France
- University of Marne la Vallée France
- University of Paris-Sud France
combinatorial Hopf algebras, Symmetric functions and generalizations, Connections of Hopf algebras with combinatorics, quasi-symmetric functions, mould calculus, Functional analytic methods in summability, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, noncommutative symmetric functions, Combinatorics (math.CO), resurgent functions
combinatorial Hopf algebras, Symmetric functions and generalizations, Connections of Hopf algebras with combinatorics, quasi-symmetric functions, mould calculus, Functional analytic methods in summability, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, noncommutative symmetric functions, Combinatorics (math.CO), resurgent functions
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