Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions   Revisited
  We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed. 
Gerard H. E. Duchamp, Florent Hivert, Jean-Christophe Novelli,   Jean-Yves Thibon