Schubert polynomials for the affine Grassmannian
Combinatorics
2007-05-23 v2 Algebraic Geometry
Abstract
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant and Kumar's nilHecke ring, work of Peterson on the homology of based loops on a compact group, and earlier work of ours on non-commutative k-Schur functions.
Cite
@article{arxiv.math/0603125,
title = {Schubert polynomials for the affine Grassmannian},
author = {Thomas Lam},
journal= {arXiv preprint arXiv:math/0603125},
year = {2007}
}
Comments
24 pages. Section 4 rewritten; examples and references added or updated