A Schubert calculus recurrence from the noncomplex W-action on G/B

TL;DR

This paper introduces a recurrence relation for calculating structure constants in the equivariant cohomology of flag manifolds, leveraging the non-complex Weyl group action, simplifying computations of individual constants.

Contribution

It presents a new recurrence method for structure constants in equivariant cohomology using non-complex Weyl group actions, reducing the need for full product calculations.

Findings

Recurrence relation for structure constants in equivariant cohomology.

Method simplifies computation of individual constants.

Recurrence is often positive, aiding calculations.

Abstract

In this paper, as in our previous "Descent-cycling in Schubert calculus" math.CO/0009112, we study the structure constants in equivariant cohomology of flag manifolds G/B. In this one we give a recurrence (which is frequently, but alas not always, positive) to compute these one by one, using the non-complex action of the Weyl group on G/B. Probably the most noteworthy feature of this recurrence is that to compute a particular structure constant c_{lambda,mu}^nu, one does not have to compute the whole product S_lambda * S_mu.