$g$-vectors and $DT$-$F$-polynomials for Grassmannians
Representation Theory
2026-05-19 v4 Algebraic Geometry
Abstract
We review -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 -vectors of the Pl\"ucker coordinates with respect to the triangular initial seed and 2) we express the -polynomials associated with the Donaldson--Thomas transformation in terms of -dimensional Young diagrams thus providing a new proof for a theorem of Daping Weng.
Keywords
Cite
@article{arxiv.2410.01037,
title = {$g$-vectors and $DT$-$F$-polynomials for Grassmannians},
author = {Sarjick Bakshi and Bernhard Keller},
journal= {arXiv preprint arXiv:2410.01037},
year = {2026}
}
Comments
38 pages. V4: Final version, To appear in Mathematische Zeitschrift