A Littlewood-Richardson rule for partial flag varieties. preprint

Abstract. This paper studies the geometry of one-parameter specializations in partial ag varieties. The main result is a positive, geometric rule for multiplying Schubert cycles in the cohomology of partial ag varieties. This rule can be interpreted as a generalization of Pieri's rule to arbitrary products and arbitrary partial ag varieties. It has numerous applications to geometry, representation theory and the theory of symmetric functions. Content