Multiplication in the cohomology of Grassmannians via Gröbner bases

Abstract

In order to gain better understanding of the multiplication in the integral cohomology of the complex Grassmann manifold G<inf>k,n</inf>(C) (in the Borel picture) a minimal strong Gröbner basis for the ideal I<inf>k,n</inf> determining this cohomology is obtained. These results are applied to obtain recurrence relations among Kostka numbers which completely determine these numbers. Corresponding results for real Grassmann manifolds are also presented.