Equivariant K-theory of Grassmannians

The combinatorics of the cohomology ring of Grassmannians has long been known to be governed by the Littlewood-Richardson rule, which was (re)formulated and proved by Schützenberger in the 1970's via the theory of jeu de taquin. I'll describe our recent extensions of his rule to equivariant cohomology and (separately) to K-theory. Then I'll give a conjectural unification to equivariant K-theory. This is joint work with Hugh Thomas.