Affine Stanley symmetric functions

Lam has recently summarized the point of view that "every affine Schubert class is a Schur-positive symmetric function." These symmetric functions for Lie types A and C were found by Lam and Lam, Schilling and Shimozono. In the cohomology case, one recovers a class of symmetric functions called affine Stanley symmetric functions, so-called because they generalize finite Stanley symmetric functions given by Stanley (type A) and Fomin and Kirillov (type B). I will discuss this and research in progress to define affine Stanley symmetric functions of the orthogonal groups.