2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110072Confirming 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.24 pages. Section 4 rewritten; examples and references added or updatedCombinatoricsAlgebraic Geometry05E05; 14N15text