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

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.

10 pages

References in corpus (1)

• Descent-cycling in Schubert calculus

Cited by in corpus (14)

• K-theoretic analogues of factorial Schur P- and Q-functions
• Hook formulas for skew shapes I. $q$-analogues and bijections
• Double Schubert polynomials for the classical groups
• Chern-Schwartz-MacPherson classes for Schubert cells in flag manifolds
• Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory
• Cohomology of GKM Fiber Bundles
• Permutation actions on equivariant cohomology
• The cohomology rings of regular nilpotent Hessenberg varieties in Lie type A
• A combinatorial rule for (co)minuscule Schubert calculus
• Littlewood-Richardson coefficients for reflection groups
• Quiver coefficients are Schubert structure constants
• Poset pinball, highest forms, and (n-2,2) Springer varieties
• Torus actions, localization and induced representations on cohomology
• Root-theoretic Young diagrams and Schubert calculus: planarity and the adjoint varieties