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Abstract

Speaker: Nantel Bergeron, York University

Title: Grothendick bialgebra, Partition lattices and symmetric functions in noncommutative variables

Abstract:

We show that the Grothendick 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.

If we have enough time we will the discuss this structure as a twisted bialgebra.

It is joint work with C. Hohlweg, M. Rosas and M. Zabrocki.



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