A filtration of the symmetric function space and new Schur functions.
Abstract: I will discuss a number of classical properties
of the Schur function basis revealing the importance of combinatorics
in symmetric function theory. I will then consider a filtration of
the symmetric function space, and introduce new symmetric functions
appearing, from their combinatorial properties, to be
the Schur functions of the subspaces associated to this filtration.
I will finish by discussing the connection between these new symmetric
functions and Macdonald polynomials.