Transition equations for isotropic flag manifolds Original Research Article

In analogy with transition equations for type A Schubert polynomials given by Lascoux and Schützenberger (1982), we give recursive formulas for computing representatives of the Schubert classes for the isotropic flag manifolds. These representatives are exactly the Schubert polynomials found in Billey and Haiman (1995). This new approach to finding Schubert polynomials is very closely related to the geometry of the flag manifold and has the advantage that it does not require explicit computations with divided difference operators. The generalized transition equations also lead to a recursion for Stanley symmetric functions and a new proof of Chevalleyʹs intersection formula for Schubert varieties. The proofs involve a careful study of the Bruhat order for the Weyl groups and two simple lemmas for applying divided difference operators.