ALGORITHM FOR MULTIPLYING SCHUBERT CLASSES

Abstract

Based on the formula for multiplying Schubert classes obtained in [17], we develop an algorithm computing the product of two arbitrary Schubert classes in a flag manifold G/H, where G is a compact connected Lie group and H ⊂ G is the centralizer of a one-parameter subgroup in G. Since all Schubert classes on G/H constitute a basis for the integral cohomology H*(G/H), the algorithm gives also a method to compute the integral cohomology ring H*(G/H) independent of the classical spectral sequence method of Leray and Borel [32, 33, 8, 9].