## The Hopf algebra of non-commutative symmetric functions

### Mike Zabrocki, (York University)

Abstract: We will give some details of recent results concerning the
space of symmetric functions in non-commuting variables (refered to as NCSF).
This algebra was recently considered by Rosas-Sagan
where they defined and developed bases which are analogous
to those which exist for the (commutative) symmetric functions.

We will try to make clear in this exposition the relationship between the
space NCSF and the space of non-commutative symmetric functions
of Gelfand-Krob-Lascoux-Leclec-Retakh-Thibon-et al. We will also introduce
the notion of a fundamental basis for NCSF which in some sense is
analogous to the Schur functions on the level of symmetric functions.

This is joint work with Nantel Bergeron.

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