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## Combinatorial Hopf Algebra

### Nantel Bergeron

CRC, York University

###
Thursday, November 10, 2005

L01 Carson Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: ** Combinatorial Hopf algebras are graded connected
Hopf algebras with basis indexed by combinatorial objects. There has
been renewed interest in these spaces in recent years
(e.g. Conne-Kreiner Hopf algebra of trees or Loday-Ronco Hopf algebra)
One particularly interesting aspect of recent work has been to realize
a given combinatorial Hopf algebra as the Grothendieck Hopf algebra of
a tower of algebras.

The prototypical example is the Hopf algebra
of symmetric functions viewed, via the Frobenius characteristic map,
as the Grothendieck Hopf algebras of the modules of all symmetric
group algebras. The multiplication is given via induction and the
comultiplication is the sum over some restrictions. The Schur
symmetric functions are then canonically defined as the Frobenius
image of the simple modules.

There are many more examples of this
kind of connection

This talk will be accessible to graduate students.