Mihail Tarigradschi "Classification of Grassmannian Schubert varieties up to      isomorphism"
Channel: Schubert Seminar
Date: 12/12/2022

Abstract: For the Grassmannian variety of m-dimensional subspaces      of an n-dimensional complex vector space, one can index its Schubert subvarieties by considering Young diagrams that fit inside a rectangle of m rows and n-m columns. It is well-known that a Young diagram and its transpose determine isomorphic Schubert varieties, furthermore the same Young diagram determines isomorphic varieties in potentially different Grassmannians. In this talk, we establish the converse, that an isomorphism of Schubert varieties implies that their Young diagrams are identical or tranposes of each other. This is joint work with Weihong Xu. Time permitting, we discuss possible generalizations to other flag varieties G/P.