Workshop on Combinatorics of Enumerative Geometry

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 shape $λ$. The structure of Springer fibers is entwined with the combinatorics of these tableaux and many open questions about the geometry of individual components remain open. In this talk, we study when components of a Springer fiber are also Richardson varieties. We give a precise characterization in terms of the associated tableaux. This answers a question raised by Springer regarding the cohomology class of each such component. This talk is based on joint work with Steven Karp.