Algorithm for Multiplying Schubert Classes

Based on the multiplicative rule of Schubert classes obtained in [Du3], we present an algorithm computing the product of two arbitrary Schubert classes in a flag variety 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 an basis for the integral cohomology H∗(G/H), the algorithm gives a method to compute the cohomology ring H∗(G/H) independent of the classical spectral sequence method due to Leray [L1,L2] and Borel [Bo1, Bo2]. 2000 Mathematical Subject Classification: 14N15; 14M10 (55N33; 22E60).