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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2110.15940 |
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| _version_ | 1866910581492023296 |
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| author | Kuwata, Ken |
| author_facet | Kuwata, Ken |
| contents | Imanishi, Jinzenji and Kuwata provided a recipe for computing Euler number of Grassmann manifold $G(k,N)$ using physical model and its path-integral [S.Imanishi, M.Jinzenji and K.Kuwata, Journal of Geometry and Physics, Volume 180, October 2022, 104623]. They demonstrated that the cohomology ring of $G(k,N)$ is represented by fermionic variables. In this study, using only fermionic variables, we computed an integral of the Chern classes of the dual bundle of the tautological bundle on $G(k,N)$. In other words, the intersection number of the Schubert cycles is obtained using the fermion integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_15940 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Schubert Calculus via Fermionic Variables Kuwata, Ken Algebraic Geometry High Energy Physics - Theory Mathematical Physics Imanishi, Jinzenji and Kuwata provided a recipe for computing Euler number of Grassmann manifold $G(k,N)$ using physical model and its path-integral [S.Imanishi, M.Jinzenji and K.Kuwata, Journal of Geometry and Physics, Volume 180, October 2022, 104623]. They demonstrated that the cohomology ring of $G(k,N)$ is represented by fermionic variables. In this study, using only fermionic variables, we computed an integral of the Chern classes of the dual bundle of the tautological bundle on $G(k,N)$. In other words, the intersection number of the Schubert cycles is obtained using the fermion integral. |
| title | Schubert Calculus via Fermionic Variables |
| topic | Algebraic Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2110.15940 |