Nantel Bergeron and Mike

Multiplicative structures of the immaculate basis of non-commutative symmetric functions

Q and Q, T-analogs of Non-commutative Symmetric Functions

We introduce two families of non-commutative symmetric functions that have analogous properties to the Hall-Littlewood and Macdonald symmetric functions.

Expansions of k-Schur Functions in the Affine nilCoxeter Algebra

We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.

A non-commutative generalization of k-Schur functions

We introduce non-commutative analogues of k-Schur functions of Lapointe-Lascoux and Morse. We give an explicit formulas for the expansions of non-commutive functions with one and two parameters in terms of these new functions. These results are similar to the conjectures existing in the commutative case.

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.