Mould calculus, polyhedral cones, and characters of combinatorial Hopf algebras. (Q394798)

The Hopf algebra of noncommutative symmetric functions \(\mathbf{Sym}\) can be interpreted as a Hopf algebra of alien operators, in the sense of Ecalle's mould calculus and resurgence theory. A method of construction of characters of \(\mathbf{Sym}\) based on these ideas is described, by means of integrals on certain polyhedral cones. This result is also extended to the Hopf algebra of quasi-symmetric functions, the Hopf algebras of set compositions \(\mathbf{WQSym}\) and of packed matrices \(\mathbf{MQsym}\). A new family of Lie idempotents is derived from the interpretation of \(\mathbf{Sym}\) from alien calculus.