Algebraic Geometry and Combinatorics Seminar: Tight pairs, Kumar's criterion, inversion arrangements, and Bruhat intervals in type A and beyond

Abstract: Motivated by questions in representation theory, Lapid defined the notion of a tight pair of permutations and showed that tight pairs indexed smooth points in Schubert varieties.  His proof is entirely combinatorial and he asked for a geometric context for his statement.  I'll describe a conjecture based on Kumar's criterion for smoothness using restriction of cohomology classes.  The permutations that form a tight pair with the identity have also come up in other contexts.  Finally I'll also describe a potential generalization to other simple Lie groups.

Host: Martha Precup