$g$-vectors and $DT$-$F$-polynomials for Grassmannians
| Autor: | Bakshi, Sarjick, Keller, Bernhard |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 Pl\"ucker 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. Comment: 34 pages |
| Databáze: | arXiv |
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