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

2003/06/20 by Allen Knutson, Knutson, Allen · 1 citation
Mathematics · #14M15 14N15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #math.CO #msc:14M15 #msc:14N15

paper · pdf · doi:10.48550/arxiv.math/0306304

10 pages

arxiv created 2003/06/20 · openalex publication_date 2003/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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,muⁿu, one does not have to compute the whole product S_lambda * S_mu.

Cited by

• Permutation actions on equivariant cohomology

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