Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras

Details Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras

2011-09-08

arxiv.org/abs/1109.1634v1

Mathematics

Combinatorics

45 pages

Scientific paper

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.

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