Titile:  Cohomological Consequences of The Pattern Map





Abstract: Billey and Braden defined maps on flag manifolds that are the geometric counterpart of permutation patterns. A section of their map is an embedding of flag manifold of a Levi subgroup into the full flag manifold. We give two expressions for the induced map on cohomology. One is in terms of generators  and the other is in terms of the Schubert basis.  We show that the coefficients in the second expression are naturally Schubert structure  constants and therefore positive. Similar results hold for K-theory, thereby generalizing known formulas in type A for cohomology and K-theory