Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables

Nantel Bergeron, Christophe Hohlweg, Mercedes Rosas, Mike Zabrocki

Published 2005-06-17Version 1

We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra.