A t-generalization for Schubert Representatives of the Affine   Grassmannian
  We introduce two families of symmetric functions with an extra parameter t that specialize to Schubert representatives for cohomology and homology of the affine Grassmannian when t = 1. The families are defined by a statistic on combinatorial objects associated to the type-A affine Weyl group and their transition matrix with Hall-Littlewood polynomials is t-positive. We conjecture that one family is the set of k-atoms. 
Avinash J. Dalal, Jennifer Morse
math.CO math.AG