Thomas Lam, Symmetric functions and variations on tableaux

It is well known that the the central objects in the theory of symmetric functions, Schur functions, are generating functions of semistandard Young tableaux. We present a collection of generalizations of semistandard tableaux. The generating functions of these tableaux are symmetric functions occurring in the study of the (co)homology of the affine Grassmannian, and the K-(co)homology of the Grassmanian.