Last update: 25 June 2013
These notes are the fruit of the author's attempts to understand and develop from scratch the elegant theory of Schubert polynomials created by A. Lascoux and M.P. Schützenberger in recent years. Most of the results expounded here occur somewhere in the publications of these authors, though not always accompanied by proof, and I have not attempted to give chapter and verse at each point. Brief indications to the literature will be found ill the notes and references at the end.
Topics not covered in these notes include (i) the interpretation of Schubert polynomials as traces of functors (from filtered vector spaces to vector spaces) for which we refer to [KPr1986]; and (ii) the non-commutative theory, for which we refer to [LSc1989].
Most of this material was presented in a course of lectures at the University of California, San Diego in the winter quarter of 1990, and I would like to take this opportunity to thank the audience, especially Adriano Garsia and Jeff Remmel, for their support.
San Diego, 1991, I.G. Macdonald
This is a typed excerpt of the book Notes on Schubert Polynomials by I. G. Macdonald.