Transition equations for isotropic flag manifolds

In analogy with transition equations for type Schubert polynomials given by Lascou and Schutzenberger s 14 , we give recursive formulas for computing representatives of the Schubert classes for the isotropic ag manifolds. These representatives are e actly the Schubert polynomials found in 2 . This new approach to nding Schubert polynomials is very closely related to the geometry of the ag manifold and has the advantage that it does not require e plicit computations with divided di erence operators. The generalized transition equations also lead to a recursion for Stanley symmetric functions and a new proof of Chevalley s 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 di erence operators.