## Symmetric Functions in Noncommuting Variables

### Mercedes H. Rosas (joint work with Bruce Sagan)

Departamento de Matematicas
Universidad Simon Bolivar
http://www.ma.usb.ve/~mrosas/

Abstract:

Consider the algebra of formal power series in countable many noncommuting
variables over the rationals. The subalgebra \Pi(x) of symmetric functions
in noncommuting variables consists of all elements invariant under
permutations of the variables and of bounded degree. We develop a theory
of such functions analogous to the ordinary theory of symmetric functions.
In particular, we define analogs of the monomial, power sum, elementary,
and complete homogeneous, and Schur symmetric functions as well as
investigating their properties.

A preprint can be downloaded at:

http://www.ma.usb.ve/~mrosas/articles/articulos.html

Slides for the talk