Combinatorics Seminar: Which Components of Springer Fibers are Richardson Varieties?

Abstract: Springer fibers are subvarieties of the flag variety parameterized by partitions. They are central objects of study in geometric representation theory. Given a partition λ, one of the key conclusions of Springer theory is that the top dimensional components of the associated Springer fiber are indexed by standard tableaux of the shape λ. In this talk, we study when components of a Springer fiber are also Richardson varieties, which are themselves an important collection of subvarieties of the flag variety indxed by paris of permutations. We give a precise characterization of such components in terms of the associated tableaux. This talk is based on joint work with Steven Karp.