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

作者：Menous Frederic; Novelli Jean Christophe; Thibon Jean Yves^*

来源：Advances in Applied Mathematics, 2013, 51(2): 177-227.

DOI：10.1016/j.aam.2013.02.003

• Combinatorial Hopf algebras
• Noncommutative symmetric functions
• Quasi-symmetric functions
• Polyhedral cones
• Mould calculus
• Resurgent functions

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 quasi-symmetric 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 a descent algebras is derived from this interpretation.

• 出版日期2013-7