Let G=GL(n), B the subgroup of upper-triangular matrices, and K=GL(p) x GL(q) where p+q=n. The group K acts with finitely many orbits on the flag variety G/B, and one can study the closures of K-orbits just as one studies Schubert varieties, which are the closures of B-orbits. The set of K-orbits is parameterized by combinatorial objects known as (p,q)-clans. I will explain an older theorem relating interval pattern avoidance on permutations and singularities of Schubert varieties and how to extend this relationship to (p,q)-clans and K-orbit closures.

This is joint work with Ben Wyser and Alexander Yong.