Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables

  • N. Bergeron
  • C. Hohlweg
  • M. Rosas
  • M. Zabrocki

Abstract

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.

Published
2006-08-25
Article Number
R75