A family of symmetric polynomials arose in our study of an
open problem regarding tableaux and Macdonald polynomials.
We will discuss this problem and see how it led us to
explicit combinatorial rules for calculating in both the
homology and cohomology of the affine Grassmannian. Our
results suggest an 'affine' tableaux approach to the
Macdonald problem as well as enumerative geometric questions
concerning certain Gromov-Witten invariants.
No background in Macdonald polynomials, geometry or Schubert
calculus will be assumed.
Joint work with Lapointe and with Lam, Lapointe, and Shimozono