  We establish combinatorial and inductive formulas for Kazhdan-Lusztig
polynomials associated to covexillary elements in classical types, extending
results of Boe, Lascoux-Sch\"{u}tzenberger, 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.
