Geometric construction of Kashiwara crystals on multiparameter persistence
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908477525327872 |
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| author | Hiraoka, Yasuaki Yahiro, Kohei |
| author_facet | Hiraoka, Yasuaki Yahiro, Kohei |
| contents | We establish a geometric construction of Kashiwara crystals on the irreducible components of the varieties of multiparameter persistence modules. Our approach differs from the seminal work of Kashiwara and Saito, as well as subsequent related works, by emphasizing commutative relations rather than preprojective relations for a given quiver. Furthermore, we provide explicit descriptions of the Kashiwara operators in the fundamental cases of 1- and 2-parameter persistence modules, offering concrete insights into the crystal structure in these settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric construction of Kashiwara crystals on multiparameter persistence Hiraoka, Yasuaki Yahiro, Kohei Representation Theory Algebraic Geometry Rings and Algebras 16G20, 55N31 We establish a geometric construction of Kashiwara crystals on the irreducible components of the varieties of multiparameter persistence modules. Our approach differs from the seminal work of Kashiwara and Saito, as well as subsequent related works, by emphasizing commutative relations rather than preprojective relations for a given quiver. Furthermore, we provide explicit descriptions of the Kashiwara operators in the fundamental cases of 1- and 2-parameter persistence modules, offering concrete insights into the crystal structure in these settings. |
| title | Geometric construction of Kashiwara crystals on multiparameter persistence |
| topic | Representation Theory Algebraic Geometry Rings and Algebras 16G20, 55N31 |
| url | https://arxiv.org/abs/2504.14844 |