$g$-vectors and $DT$-$F$-polynomials for Grassmannians
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909053033119744 |
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| author | Bakshi, Sarjick Keller, Bernhard |
| author_facet | Bakshi, Sarjick Keller, Bernhard |
| contents | We review $\mathrm{Hom}$-infinite Frobenius categorification of cluster algebras with coefficients and use it to give two applications of Jensen--King--Su's Frobenius categorification of the Grassmannian: 1) we determine the $g$-vectors of the Plücker coordinates with respect to the triangular initial seed and 2) we express the $F$-polynomials associated with the Donaldson--Thomas transformation in terms of $3$-dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $g$-vectors and $DT$-$F$-polynomials for Grassmannians Bakshi, Sarjick Keller, Bernhard Representation Theory Algebraic Geometry 13F60, 18G80, 14M15 We review $\mathrm{Hom}$-infinite Frobenius categorification of cluster algebras with coefficients and use it to give two applications of Jensen--King--Su's Frobenius categorification of the Grassmannian: 1) we determine the $g$-vectors of the Plücker coordinates with respect to the triangular initial seed and 2) we express the $F$-polynomials associated with the Donaldson--Thomas transformation in terms of $3$-dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng. |
| title | $g$-vectors and $DT$-$F$-polynomials for Grassmannians |
| topic | Representation Theory Algebraic Geometry 13F60, 18G80, 14M15 |
| url | https://arxiv.org/abs/2410.01037 |