The University of Michigan Combinatorics Seminar
Fall 2002
November 1, 4:10-5:00, 3866 East Hall





Schubert polynomials and Quiver formulas

Alexander Yong

University of Michigan




Abstract

Fulton's Universal Schubert polynomials represent general degeneracy loci for maps of vector bundles with rank conditions coming from a permutation. The Buch-Fulton Quiver formula expresses this polynomial as an integer linear combination of products of Schur polynomials in the differences of the bundles. We present a positive combinatorial formula for the coefficients which are known to directly generalize the Littlewood-Richardson coefficients. Our formula counts sequences of semi-standard Young tableaux satisfying certain conditions. One consequence is a nonrecursive description of the Fomin-Gelfand-Postnikov quantization map for flag manifolds and the generalization to partial flag manifolds due to Ciocan-Fontanine.

This is joint work with Anders Buch, Andrew Kresch and Harry Tamvakis.