Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables
Combinatorics
2010-04-01 v1 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.math/0506360,
title = {Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables},
author = {Nantel Bergeron and Christophe Hohlweg and Mercedes Rosas and Mike Zabrocki},
journal= {arXiv preprint arXiv:math/0506360},
year = {2010}
}
Comments
17 pages