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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2305.04045 |
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| _version_ | 1866910368701349888 |
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| author | Kadhem, Fayadh |
| author_facet | Kadhem, Fayadh |
| contents | In the construction of a cluster algebra on the homogeneous coordinate ring of a partial flag variety by Geiß, Leclerc and Schr{ö}er, they defined a special map denoted by ``tilde". This map lifts each element $f$ of the coordinate ring of a Schubert cell uniquely to an element $\widetilde{f}$ of the (multi-homogeneous) coordinate ring of the corresponding partial flag variety. The significance of this map appears from its essential role; it lifts the cluster algebra of the coordinate ring of a cell to a cluster algebra living in the coordinate ring of the corresponding partial flag variety. This paper takes a closer look at this map and gives an explicit algorithm to calculate it for the \textit{generalized minors}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04045 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | GLS homogenization tilde map Kadhem, Fayadh Rings and Algebras In the construction of a cluster algebra on the homogeneous coordinate ring of a partial flag variety by Geiß, Leclerc and Schr{ö}er, they defined a special map denoted by ``tilde". This map lifts each element $f$ of the coordinate ring of a Schubert cell uniquely to an element $\widetilde{f}$ of the (multi-homogeneous) coordinate ring of the corresponding partial flag variety. The significance of this map appears from its essential role; it lifts the cluster algebra of the coordinate ring of a cell to a cluster algebra living in the coordinate ring of the corresponding partial flag variety. This paper takes a closer look at this map and gives an explicit algorithm to calculate it for the \textit{generalized minors}. |
| title | GLS homogenization tilde map |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2305.04045 |