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<p>We review <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{Hom}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Hom</mtext> </math></EquationSource> </InlineEquation>-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 <i>g</i>-vectors of the Plücker coordinates with respect to the triangular initial seed and (2) we express the <i>F</i>-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.</p>

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g-vectors and DT-F-polynomials for Grassmannians via additive categorification

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Sarjick Bakshi,
  • Bernhard Keller

摘要

We review \(\textrm{Hom}\) 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.