Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables
Copyright policy )Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables
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.
- University of Quebec Canada
- University of Seville Spain
- York University Canada
- UNIVERSITE DE MONTREAL Canada
Symmetric functions and generalizations, Schur function, Mathematics - Rings and Algebras, Hecke algebras and their representations, noncommutative variables, 05E05, 05E10, 16G30, 16S34, 16W30, (secondary), Rings and Algebras (math.RA), Combinatorial aspects of representation theory, 16S99 (Primary); 05E05, 05E10, 16G30, 16S34, 16W30, (secondary), FOS: Mathematics, Mathematics - Combinatorics, partition lattices, Combinatorics (math.CO), Grothendieck bialgebras, Representations of associative Artinian rings, 16S99 (Primary)
Symmetric functions and generalizations, Schur function, Mathematics - Rings and Algebras, Hecke algebras and their representations, noncommutative variables, 05E05, 05E10, 16G30, 16S34, 16W30, (secondary), Rings and Algebras (math.RA), Combinatorial aspects of representation theory, 16S99 (Primary); 05E05, 05E10, 16G30, 16S34, 16W30, (secondary), FOS: Mathematics, Mathematics - Combinatorics, partition lattices, Combinatorics (math.CO), Grothendieck bialgebras, Representations of associative Artinian rings, 16S99 (Primary)
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