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Grothendieck bialgebras, partition lattices, and symmetric functions in noncommutative variables. (English) Zbl 1098.05079

Summary: 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.

MSC:

05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
16G10 Representations of associative Artinian rings
20C08 Hecke algebras and their representations

Keywords:

Schur function