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arXiv · 2312.02574

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

Nicolas Ressayre·Luca Francone
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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 $\odot_0$, on the cohomology $\mathrm{H}^{*}(X,\mathbf{Z})$, 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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Nicolas Ressayre, Luca Francone. 2023-12-05. Intersection multiplicity one for the Belkale-Kumar product in G/B. https://arxiv.org/abs/2312.02574

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