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 |