Kostant polynomials and the cohomology ring for G/B

Abstract

The Schubert calculus for G=B can be completely determined by a certain matrix related to the Kostant polynomials introduced in [1][Section 5]. The polynomials are defined by vanishing properties on the orbit of a regular point under the action of the Weyl group. For each element w in the Weyl group the polynomials also have non-zero values on the orbit points corresponding to elements which are larger in the Bruhat order than w. Our main theorem is an explicit formula for these values. The matrix of orbit values can be used to determine the cup product for the cohomology ring for G=B, using only linear algebra or as described in [13].