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Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables

Nantel Bergeron·Christophe Hohlweg·Mercedes Rosas·Mike Zabrocki
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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.

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Nantel Bergeron, Christophe Hohlweg, Mercedes Rosas, Mike Zabrocki. 2005-06-17. Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables. https://arxiv.org/abs/math/0506360

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