Combinatorics Seminar: "The isomorphism problem for Schubert varieties."

Abstract: Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group.  In this talk, I will discuss recent work with William Slofstra where we give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are isomorphic, in terms of the Cartan matrix and reduced words for the indexing Weyl group elements. As a corollary, we show that two such Schubert varieties are isomorphic if and only if there is an isomorphism between their integral cohomology rings that preserves the Schubert basis.  As an application, we show that the isomorphism classes of Schubert varieties in a given flag variety are controlled by graph automorphisms of the Dynkin diagram.
 

Host: Martha Precup