Schubert polynomials for the affine Grassmannian

Details Schubert polynomials for the affine Grassmannian Schubert polynomials for the affine Grassmannian

2006-03-06

arxiv.org/abs/math/0603125v2

Mathematics

Combinatorics

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

Scientific paper

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.

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