A Littlewood-Richardson rule for Grassmannian Permutations

TL;DR

This paper introduces a combinatorial rule for calculating intersection numbers on flag manifolds, extending the Littlewood-Richardson rule from Grassmannians to more general flag varieties.

Contribution

It generalizes the classical Littlewood-Richardson rule to a broader class of geometric objects, providing a new combinatorial tool for intersection theory.

Findings

Provides a new combinatorial rule for flag manifolds

Extends known rules from Grassmannians to flag varieties

Facilitates computation of intersection numbers in algebraic geometry

Abstract

We give a combinatorial rule for computing intersection numbers on a flag manifold which come from products of Schubert classes pulled back from Grassmannian projections. This rule generalizes the known rule for Grassmannians.