Intersection multiplicity one for the Belkale-Kumar product in G/B

2023/12/05 by Nicolas Ressayre, Luca Francone, Ressayre, Nicolas +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.02574

openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the complete flag variety X of a complex semisimple algebraic group G. We show that the structure coefficients of the Belkale-Kumar product \odot₀, on the cohomology H^*(X,Z), are all either 0 or 1. We also derive some consequences. The proof that is mainly geometric also uses new combinatorial results on root systems. Moreover, it is uniform and avoids case by case considerations.

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