Intersection multiplicity one for the Belkale-Kumar product in G/B
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913761257848832 |
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| author | Ressayre, Nicolas Francone, Luca |
| author_facet | Ressayre, Nicolas Francone, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02574 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Intersection multiplicity one for the Belkale-Kumar product in G/B Ressayre, Nicolas Francone, Luca Algebraic Geometry Combinatorics Representation Theory 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. |
| title | Intersection multiplicity one for the Belkale-Kumar product in G/B |
| topic | Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2312.02574 |