By Laurent Manivel, John R. Swallow

ISBN-10: 0821821547

ISBN-13: 9780821821541

This article grew out of a sophisticated direction taught by means of the writer at the Fourier Institute (Grenoble, France). It serves as an advent to the combinatorics of symmetric features, extra accurately to Schur and Schubert polynomials. additionally studied is the geometry of Grassmannians, flag kinds, and particularly, their Schubert kinds. This booklet examines profound connections that unite those topics.

The e-book is split into 3 chapters. the 1st is dedicated to symmetric capabilities and particularly to Schur polynomials. those are polynomials with confident integer coefficients during which every one of the monomials correspond to a tender tableau with the valuables of being "semistandard". the second one bankruptcy is dedicated to Schubert polynomials, that have been came across by means of A. Lascoux and M.-P. Schützenberger who deeply probed their combinatorial houses. it really is proven, for instance, that those polynomials help the delicate connections among difficulties of enumeration of decreased decompositions of variations and the Littlewood-Richardson rule, a very efficacious model of that may be derived from those connections. the ultimate bankruptcy is geometric. it's dedicated to Schubert kinds, subvarieties of Grassmannians, and flag forms outlined via convinced prevalence stipulations with mounted subspaces.

This quantity makes obtainable a couple of effects, making a sturdy stepping stone for scaling extra bold heights within the region. The author's cause used to be to stay straightforward: the 1st chapters require no past wisdom, the 3rd bankruptcy makes use of a few rudimentary notions of topology and algebraic geometry. For this cause, a finished appendix at the topology of algebraic types is equipped. This booklet is the English translation of a textual content formerly released in French.