k-Double Schur functions and equivariant (co)homology of the affine   Grassmannian
  The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions called k-double Schur functions and affine double Schur functions. 
Thomas Lam and Mark Shimozono
math.CO math.AG