Covexillary Schubert varieties and Kazhdan–Lusztig polynomials

Abstract

We establish combinatorial and inductive formulas for Kazhdan–Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux–Schützenberger, Sankaran–Vanchinathan, and Zelevinsky for Grassmannians of classical types. The proof uses intersection cohomology theory and the isomorphism of Kazhdan–Lusztig varieties from Anderson–Ikeda–Jeon–Kawago.