arXiv:math/0603125 Abstract

arXiv:math/0603125 [math.CO]Abstract References Reviews Resources

Schubert polynomials for the affine Grassmannian

Published 2006-03-06, updated 2006-03-31Version 2

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.

Comments: 24 pages. Section 4 rewritten; examples and references added or updated

Categories: math.CO, math.AG

Subjects: 05E05, 14N15

Keywords: affine grassmannian, schubert polynomials, affine schur functions, kumars nilhecke, identify polynomial representatives

Related articles: Most relevant | Search more

arXiv:0901.1506 [math.CO] (Published 2009-01-12, updated 2009-08-31)

K-theory Schubert calculus of the affine Grassmannian

Thomas Lam, Anne Schilling, Mark Shimozono

arXiv:1705.09649 [math.CO] (Published 2017-05-26)

A Demazure crystal construction for Schubert polynomials

Sami Assaf, Anne Schilling

arXiv:2102.11179 [math.CO] (Published 2021-02-22)