Schubert Polynomials for the affine Grassmannian of the symplectic group

In this talk we present a combinatorial description of the analogue of affine Stanley symmetric functions for type C, a subset of which provides a basis for the cohomology ring of the affine flag variety. Lam introduced affine Stanley symmetric functions for type A, which are dual to the k-Schur functions of Lapointe, Lascoux and Morse. The combinatorics in the type C case involves the notion of Zs. This also allows us to derive a Pieri rule for homology classes. This talk is based on joint work with Thomas Lam and Mark Shimozono arXiv.org:math.CO/0710.2720